Calculus Tutorial Playlist
Lección 2 de 293 · Parent Functions Transformations & Graphs – End Behavior / Domain and Range Plus Asymptotes · Estudios básicos
Parent Functions Transformations & Graphs – End Behavior / Domain and Range Plus Asymptotes
This math video tutorial provides a review of parent functions with their graphs and transformations. This video is for students who might be taking algebra 1 or 2, precalculus or even calculus. This video contains plenty of notes, examples, and practice problems for you to work on.
Here is a list of topics:
1. F(x) functions and transformations
2. Horizontal Shift – Left and Right Units
3. Vertical Shift – Units Up and Down
4. Reflection about the x-axis, y-axis, and origin
5. Inverse function f-1(x)
6. Domain and Range – X and Y Values
7. Horizontal and Vertical Asymptotes
8. End Behavior – Left and Right Side
9. Linear Functions: y=x
10. Parabolas and Quadratic Functions: y=x^2 or y=x2
11. Polynomial Functions – Cubic Functions: y=x^3
12. Absolute Value Functions
13. Cube Root Functions
14. Square Root and Radical Functions
15. Rational Functions y = 1/x – Vertical and Horizontal Asymptotes
16. Exponential Functions: y=e^x
17. Logarithmic Functions – Log and Natural Log Functions y=lnx
18. Trigonometric Functions – sine, cosine, and tangent – sin cos tan
19. Inverse Trigonometric Functions y = sin^-1 x cos^-1(x) and tan^-1(x)
- (lnx)^2
- 1/sqrt(x)
- 1/x
- 1/x^2
- 2^x
- 3 step continuity test
- 3 variables
- ab
- about x axis
- about y axis
- abs x
- abs(x)
- absolute
- Absolute Extrema
- absolute min and max
- absolute minimum and maximum calculus
- Absolute Value
- absolute value functions
- absolute value of x
- acceleration
- acceleration time graph
- adding and subtracting vectors
- airplane
- algebra
- algebra 1
- algebra 2
- alternative definition of derivative
- angle
- angle of elevation
- Antiderivative
- antiderivative calculus
- antiderivatives
- antiderivatives of exponential functions
- antiderivatives of fractions
- antiderivatives of square roots
- antiderivatives of trig functions
- antidifferentiation
- ap calc
- AP Calculus
- approximate integration midpoint rule
- approximate integration simpson's rule
- approximate integraton
- approximation
- Arc Length
- arc length calculus
- arc length examples
- arc length formula
- arc length integration
- area
- area approximation
- area between curves
- area between two curves
- area between two curves respect to y
- area of shaded region
- area under a curve
- area under curve
- around non axis
- Asymptotes
- AVERAGE
- average cost
- Average Rate of Change
- average rate of change between two points
- average rate of change calculus
- average rate of change of a function
- average rate of change over an interval
- average speed
- average value
- average value of a function
- average value of a function calculus
- average value of a function on an interval using calculus
- average velocity
- Back to School
- base
- baseball diamond
- Basic
- basic integration
- basic integration formulas
- basic integration problems
- basic integration rules
- basic introduction
- basics
- between two points
- boat problem
- Box
- box and whisker plots
- business
- business calculus
- c value
- calc 2
- Calculus
- calculus 1
- calculus 1 derivatives
- calculus 1 limits
- calculus 1 review
- calculus 2
- Calculus 3
- calculus basic introduction
- calculus continuity and discontinuity
- calculus derivatives
- calculus introduction
- calculus limits
- calculus limits and continuity
- calculus limits explained
- calculus limits review
- calculus position velocity acceleration
- calculus review
- Cars
- Chain Rule
- chain rule calculus
- chain rule derivatives
- chain rule derivatives calculus
- chain rule derivatives square root
- chain rule derivatives trig functions
- chain rule examples
- chain rule with trig functions
- Channel
- circle
- circles
- closed interval
- common denominator
- Completing the Square
- complex fraction
- component form
- composite functions
- concave down
- concave up
- concavity
- concavity and inflection point
- cone
- conic sections
- conical pile
- conical tank
- conjugate
- constant
- constant c
- constant multiple rule
- continuity
- continuity basic introduction
- continuity calculus
- continuity introduction
- continuity of a function
- continuity of limits
- continuity test
- Continuous
- convergence
- convergent
- cooling
- cos
- cos^-1 (x^2)
- cos^3x
- cos(2x)
- cos(x^3)
- cos(xy)
- Cosine
- cost
- cost function
- cosx
- cot
- cot^-1 (3x)
- cotx
- critical numbers
- critical numbers calculus
- Critical Points
- critical points and extrema
- critical points and inflection points
- critical points calculus
- cross sectional volume
- cross sections
- cross sections calculus
- cross sections of solid
- csc
- cscx
- cube
- cumulative relative frequency
- curve
- curve sketching
- curve sketching asymptotes
- curve sketching calculus
- curve sketching rational functions
- curve sketching using derivatives
- curve sketching using the first and second derivatives
- cusps
- cylinder
- cylindrical shells
- cylindrical shells about x axis
- cylindrical shells about y axis
- cylindrical shells calculus
- d^2y/dx^2
- data table
- decreasing function
- definite integral
- definite integral calculus
- definite integral examples
- definite integral formula
- definite integrals
- definition of derivative
- definition of derivative 1/sqrt(x)
- definition of derivative fraction
- definition of derivative square root
- delta x
- delta y
- demand
- demand function
- demand function calculus
- Derivative
- derivative definition
- derivative of inverse functions
- derivative of inverse functions calculus
- derivative of inverse functions examples
- derivative of x^x^x
- Derivatives
- derivatives absolute value
- derivatives calculus
- derivatives chain rule
- derivatives chain rule and product rule
- derivatives limit process
- derivatives of absolute value functions
- derivatives of composite functions
- derivatives of exponential functions
- derivatives of inverse functions practice problems
- derivatives of inverse trigonometric functions
- derivatives of logarithmic functions
- derivatives of logs
- derivatives of natural logs
- derivatives of trigonometric functions
- derivatives of trigonometric functions chain rule
- derivatives power rule
- derivatives product rule
- derivatives quotient rule
- derivatives square roots
- desmos
- difference of cubes
- difference of squares
- Difference Quotient
- differences
- differentiability
- Differentiable
- differential equations
- differentials
- differentiation
- direct substitution
- discontinuity
- discontinuity calculus
- discontinuity limits
- Discontinuous
- disk method
- disk method around non axis
- disk method around x axis
- disk method around y axis
- disk method calculus
- displacement
- displacement time graph
- distance
- distance time graph
- divergence
- divergent
- domain
- domain and range
- domain and range of a function
- domain and range of a graph
- domain and range of a quadratic function
- domain and range of exponential functions
- domain and range of logarithmic functions
- domain and range of rational functions
- domain and range of trigonometric functions
- dot plots
- double angle formulas
- double angle identities
- Dr.
- du/dx
- DV
- dx
- dy
- dy/dx
- e^2x
- e^3x
- e^cos(2x)
- e^sinx
- e^x cosx
- e^x sinx
- e^x^2
- E2
- economics
- eliminating parameter
- eliminating the parameter
- elimination
- Ellipse
- end behavior
- Energy
- equation
- equation of normal line
- equation of tangent line
- equations
- equilateral triangle
- error bound
- error bound midpoint rule
- error bound simpson's rule
- error bound trapezoidal rule
- estimate
- EU
- euler's method
- euler's method calculus
- euler's method differential equations
- euler's method example
- euler's method numerical methods
- ex
- example
- examples
- explained
- exponential
- Exponential Function
- exponential functions
- exponential growth and decay
- exponential growth and decay calculus
- exponential growth and decay differential equations
- exponential growth and decay word problems
- Extrema
- extreme value theorem
- extreme values
- f f' f'' calculus
- f f' f'' graphs
- f^-1(x)
- f(a)
- f(g(x))
- f(y)
- factor
- factoring
- factoring perfect square trinomials
- factoring the gcf
- fence problems cost
- find c
- find c value
- find the equation of the tangent line at a point
- find the slope of the tangent line to the curve
- finding inflection points
- first derivative
- First Derivative Test
- First Order Differential Equations
- first order partial derivatives
- formula
- fraction
- fractions
- frequency distribution table
- frequency tables
- from the left
- from the right
- FTC
- function
- functions
- fundamental theorem
- Fundamental Theorem Of Calculus
- fundamental theorem of calculus examples
- fundamental theorem of calculus explained
- fundamental theorem of calculus part 1
- fundamental theorem of calculus part 2
- fx
- g(x)
- g(y)
- general equation
- General Solution
- given point
- graph
- graphical method
- graphing
- graphing derivatives
- graphing exponential functions
- graphing functions
- graphing functions using derivatives
- graphing inequalities
- Graphing Linear Equations
- graphing logarithmic functions
- graphing parabolas
- graphing parametric equations
- graphing plane curves
- graphing polar equations
- graphing quadratic functions
- graphing rational functions
- graphing sine and cosine functions
- graphing trignometric functions
- graphs
- greatest integer function
- greatest integer function calculus
- greatest integer function continuity
- greatest integer function examples
- greatest integer function explained
- greatest integer function graph
- greatest integer function limits
- greatest integer function limits problems
- greatest integer function problems
- h(x)
- head to tail
- head to tail method
- height
- higher order partial derivatives
- Histograms
- hole
- horizontal and vertical component
- horizontal asymptotes
- Horizontal Line
- horizontal tangent line
- horizontal tangent line calculus
- how to evaluate the limit of rational functions
- how to find angle
- hypotenuse
- Identities
- Implicit Differentiation
- implicit differentiation calculus
- implicit differentiation examples
- implicit differentiation second derivative
- implicit differentiation trig functions
- Improper Integrals
- improper integrals convergence and divergence
- increasing
- increasing and decreasing functions
- increasing and decreasing intervals
- increasing function
- indefinite integral
- indefinite integral calculus
- indefinite integral fraction
- indefinite integral square root
- indefinite integrals
- Indeterminate
- indeterminate forms
- Inequalities
- infinite discontinuity
- infinite limits
- infinite limits and asymptotes
- infinite limits and limits at infinity
- infinite limits and vertical asymptotes
- infinite limits calculus
- infinite limits examples
- infinite limits of integration
- infinite limits with radicals
- infinite limits with square roots
- infinity
- inflection points
- inflection points and concavity
- inflection points on a graph
- Initial Condition
- instantaneous acceleration
- instantaneous rate of change
- instantaneous rate of change calculus
- instantaneous rate of change of a function
- instantaneous velocity
- integral
- integrate
- integrating
- integrating by substitution
- integrating exponential functions
- integrating ln
- integrating logarithmic function
- integrating natural logarithms
- integrating natural logs
- Integration
- integration by partial fractions
- Integration By Parts
- integration by parts e^x sinx
- integration by parts lnx
- integration by parts twice
- integration by parts x^2 sinx
- integration by parts x^3 lnx
- integration by parts xe^x
- Integration By Substitution
- integration long division
- integration natural log
- integration of logarithmic functions
- integration of natural log functions
- integration techniques
- intermediate value theorem
- intermediate value theorem calculus
- intermediate value theorem explained
- intermediate value theorem for polynomials
- intermediate value theorem roots
- intermediate value theorem to find zeros
- interquartile range
- intersection
- interval
- Interval Notation
- intervals
- Introduction
- introduction to limits
- introduction to limits calculus
- inverse
- inverse cos x^2
- Inverse Function
- inverse functions
- inverse sec (1+x^2)
- inverse secx
- inverse sin 2x
- inverse tan (x/2)
- inverse trig
- inverse trig functions
- Inverse Trigonometric Functions
- isosceles right triangle
- ivt
- ivt theorem
- jump discontinuity
- L'hopital's rule
- l'hopital's rule indeterminate forms
- l'hopital's rule infinity
- l'hopital's rule limits
- L'hospital's rule
- L(x)
- ladder angle
- ladder problem
- left and right
- left endpoints
- limit
- limit process
- limits
- Limits and Continuity
- limits and derivatives
- limits at infinity
- limits at infinity with radicals
- limits basic introduction
- limits calculus
- limits direct substitution
- limits introduction
- limits numerically
- limits of integration
- limits of trigonometric functions
- limits review
- line
- linear
- linear approximation
- linear approximation and differentials
- linear approximation formula
- linear equations
- linear factors
- linear functions
- Linearization
- linearization formula
- ln
- ln(2x)
- ln(cosx)
- ln(ln(lnx))
- ln(lnx)
- ln(sinx)
- ln(x+1)
- lnx
- lnx/x
- local
- Local Extrema
- local max and min calculus
- local maximum and minimum
- local min and max
- local minimum and maximum calculus
- log(1-x)
- log(2x)
- log(x^2)
- logarithmic
- logarithmic differentiation
- logarithmic differentiation examples
- logarithmic differentiation rules
- logarithmic differentiation with exponentials
- logarithmic functions
- logarithms
- Logistic Equation
- logistic function
- logistic growth
- logistic growth differential equations
- logistic growth equation
- logistic growth formula
- logistic growth function
- logistic growth model
- logistic growth model of a population
- logistic growth problem
- logs
- long division
- lower bound
- m/s
- m/s^2
- magnitude and direction
- marginal cost
- marginal profit
- marginal revenue
- marginal revenue and marginal cost
- marginal revenue calculus
- Maths
- Max
- maxima
- maximizing profit
- maximum
- maximum profit
- Mean
- Mean Value Theorem
- mean value theorem and rolle's theorem
- mean value theorem calculus
- mean value theorem examples
- mean value theorem for derivatives
- median
- midpoint
- midpoint rule
- min
- minima
- minimize
- minimum
- minimum average cost
- minimum distance
- mixed partial derivatives
- MODE
- monomials
- motion
- moving to the left
- moving to the right
- multivariable calculus
- natural log
- natural logarithms
- natural logs
- negative velocity
- net change
- net change theorem
- newton's law of cooling
- newton's law of cooling calculus
- newton's law of cooling differential equations
- newton's law of cooling example
- newton's law of cooling problems
- newtons law
- nonremovable discontinuity
- Normal Line
- normal line and tangent line
- norman window
- Number
- number line
- Numerical Integration
- numerical integration trapezoidal rule
- numerical methods
- Object
- of e
- one sided limits
- one sided limits absolute value
- one sided limits calculus
- online graphing calculator
- open box
- open interval
- optimization
- optimization calculus
- optimization cylinder
- optimization fence problem
- optimization minimum distance
- optimization norman window
- optimization volume of a box
- organic chemistry tutor
- outliers
- over an interval
- Overview
- parabolic functions
- parallel and perpendicular lines
- parameter t
- Parametric Equations
- parametric equations calculus
- parametric equations eliminating parameter t
- parametric equations ellipse
- parametric equations introduction
- parametric equations precalculus
- parent functions
- parent functions algebra 2
- parent functions and their graphs
- parent functions and transformations
- parent functions domain and range
- parent functions precalculus
- part 1
- part 2
- Partial Derivatives
- partial derivatives calculus 3
- partial derivatives of a function of two variables
- partial derivatives quotient rule
- Partial Fraction Decomposition
- partial fraction integration
- Partial Fractions
- particle
- particle motion
- Particular Solution
- Patreon
- patreon channel
- patreon review
- patreon rewards
- patreon rewards tutorial
- patreon tutorial
- patreon tutorial video
- patreon video
- percentile
- perfect square trinomials
- Perimeter
- permutations
- perpendicular to x-axis
- perpendicular to y-axis
- physics
- piecewise
- piecewise function
- Piecewise Functions
- piecewise functions absolute value
- piecewise functions calculus
- piecewise functions continuity
- piecewise functions domain and range
- piecewise functions graphing
- piecewise functions limits
- plane curves
- point
- point discontinuity
- point slope form
- points
- points of discontinuity
- polynomial
- polynomial function
- polynomial functions
- polynomials
- population growth
- position
- position time graph
- position time graph physics
- position time graph to velocity time graph
- position velocity and acceleration
- Power
- power reducing formulas
- Power Rule
- powers
- practice
- practice problems
- Precalculus
- Price
- price function
- price function calculus
- problems
- product
- Product Rule
- product rule f(x)g(x)h(x)
- product to sum
- production level
- profit
- proof
- properties of definite integrals
- properties of definite integrals examples
- PROPERTIES OF INTEGRALS
- prove
- quadratic
- quadratic factors
- Quadratic Functions
- quartiles
- Quotient Rule
- radical
- radical functions
- radicals
- radius
- range
- Rate of Change
- rate of change of water
- rates of change
- rational
- rational function
- rational functions
- Rectangle
- rectangles
- Related Rates
- related rates calculus
- related rates problems
- relative
- Relative Extrema
- relative extrema of a function
- relative frequency
- relative growth rate
- relative growth rate calculus
- relative maximum and minimum
- removable discontinuity
- removable discontinuity calculus
- respect to x
- respect to y
- rest
- resultant
- revenue
- review
- rewards
- Riemann Sum
- riemann sum calculus
- riemann sum midpoint
- riemann sum sigma notation
- riemann sums and definite integral
- right endpoints
- rise over run
- Rolle's Theorem
- rolle's theorem and the mean value theorem
- rolle's theorem calculus
- rolle's theorem examples
- rolle's theorem explained
- roots
- Rules
- scalar
- scalar multiplication
- Scalars
- SEC
- sec^-1 (1+x^2)
- sec^3x
- sec(x^2)
- secant
- secant line
- second derivative
- second order partial derivatives
- second partial derivatives
- secx
- secxtanx
- semicircles
- Separation of variables
- separation of variables differential equations
- shaded region
- shadow problem
- shell method
- shell method around non axis
- shell method calculus
- shell method x axis
- shell method y axis
- ship problem
- sigma notation
- sigma notation calculus
- Sign
- sign chart
- sign conventions
- similar triangles
- Simpson's Rule
- simpson's rule error
- simpson's rule numerical method
- sin
- sin x
- sin^-1 (2x)
- sin^2(3x)
- sin^2x
- sin^3x
- sin^4x
- sin^5x
- sin(x+y)
- sine
- sine and cosine
- sinx
- sinx/x
- siny
- sketching derivatives
- sketching derivatives from parent function
- skewed left
- skewed right
- skewness
- Slope
- slope of normal line
- slope of tangent line
- Slope-Intercept Form
- slowing down
- snowball
- speed
- speeding up
- Sphere
- spherical balloon
- spotlight
- sqrt(x)
- sqrt(y)
- Square
- Square Root
- square root functions
- square roots
- Squeeze Theorem
- squeeze theorem calculus
- squeeze theorem calculus examples
- squeeze theorem definition
- squeeze theorem examples
- squeeze theorem explained
- squeeze theorem inequalities
- squeeze theorem limits
- squeeze theorem trig functions
- squeeze theorem with cos
- squeeze theorem with sin
- statistics
- stem and leaf plots
- Steps
- subintervals
- substitution
- sum
- summary of curve sketching
- supply
- surface area
- surface area by integration
- surface area calculus
- surface area example
- surface area explained
- surface area formula
- surface area integral
- surface area of revolution
- System of Equations
- table
- tan
- tan^-1 (x/2)
- tan^2x
- tan^3x
- tan^4x
- tan(sin4x)
- Tangent
- Tangent Line
- tangent line approximation
- tangent line problem
- tanx
- techniques
- techniques of integration
- third order partial derivatives
- three variables
- time
- time graph
- to find zeros
- total cost
- total distance
- transformations
- trapezoidal
- Trapezoidal Rule
- trapezoidal rule error bound
- trapezoidal rule numerical method
- triangle
- triangles
- trig
- trig functions
- trig identities
- trig integrals
- trig substitution
- trigonometric
- Trigonometric Functions
- trigonometric identities
- trigonometric integrals
- trigonometric integrals even powers
- Trigonometric Substitution
- trigonometric substitution completing the square
- trigonometric substitution definite integral
- Trigonometry
- Trinomials
- trough
- tutorial
- tutorial video
- Two Variables
- u-substitution
- u-substitution definite integral
- u-substitution indefinite integral
- u-substitution integration
- u-subtitution
- units
- upper bound
- vector notation
- Vectors
- vectors basics
- vectors calculus
- vectors explained
- vectors maths
- vectors physics
- vectors precalculus
- vectors review
- vectors trigonometry
- Velocity
- velocity time graph
- velocity time graph physics
- velocity time graph to acceleration time graph
- vertical asymptotes
- video
- volume
- volume flow rate
- volume of a sphere
- volume of revolution
- volume of revolution about y axis
- volume of revolution shell method
- volumes of revolution
- volumes of revolution shell method
- volumes using cross sections
- volumes using cross sections calculus
- washer method
- washer method around y axis
- washer method calculus
- washer method rotating around non axis
- washer method y axis
- water trough
- weight
- with 3 components
- with i and j
- with two functions
- Word Problems
- x axis
- x e^2x
- x^2
- x^2 e^x
- x^2 lnx
- x^2 sinx
- x^2e^x
- x^2lnx
- x^3 lnx
- x^4 sinx
- x^lnx
- x^sinx
- x^x
- x^x^x
- xcosx
- xe^x
- y axis