Transformations of Functions Problem Solving (Function Composition, Inverse Functions, & Quadratics)

A math tutorial about graphical transformations of functions and other related topics. These include function composition, function decomposition, inverse functions, and quadratic functions (factoring, quadratic formula, completing the square, vertex form). Infinite Powers, How Calculus Reveals the Secrets of the Universe: https://amzn.to/37PBMjb.

🔴 Calculus 1, Lesson 1.1: Linear Functions (3Blue1Brown SoME2): https://www.youtube.com/watch?v=lmCjnxzIals

🔴 Calculus 1, Lesson 1.2: Exponential Functions: https://www.youtube.com/watch?v=47ZqW19AjD4

🔴 Calculus 1, Lesson 1.3: Quadratic Functions, Transformations of Functions, and Function Composition: https://www.youtube.com/watch?v=1T58CnSME4g

🔴 AP Calculus AB Exam Review: Practice Exam Problems & Solutions (Multiple Choice, No Calculator): https://www.youtube.com/watch?v=2AG_Dt3x7q0

🔴 AP Calculus AB Exam Review: Free Response Practice Exam Problems & Solutions: https://www.youtube.com/watch?v=RLgUwP44V_M

🔴 AP Calculus BC Exam Review: Practice Exam (30 Question Multiple Choice, No Calculator): https://www.youtube.com/watch?v=1Q7ALcwT97A

🔴 AP Calculus BC Exam Review: Free Response Practice Exam Problems & Solutions: https://www.youtube.com/watch?v=ZWisJEDP44w

🔴 Calculus 1 Exam 1 Review Problems and Solutions (Precalculus, Limits, Continuity, Derivatives): https://www.youtube.com/watch?v=UjmvUwvd7c4

🔴 Calculus 1 Course, Lecture 1: The Big Ideas (Rates & Areas, the Infinity Principle & Circular Area): https://www.youtube.com/watch?v=2V_ehJC5QUY

🔴 Calculus 1 Course Lecture Playlist: https://www.youtube.com/playlist?list=PLmU0FIlJY-MkFrKtM0S0NLu-TxZa5jBIx

#exponential #ExponentialFunction #calculus

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(0:00) Transformations of a function graphs
(0:37) g(t) = f(t-2) (horizontal translation)
(3:00) h(t) = 2f(t+1) (vertical stretch/dilation and horizontal translation)
(6:15) j(t) = -f(t) + 1 (vertical reflection and vertical translation)
(8:32) Function composition and simplification
(16:00) Function decomposition (for the Chain Rule)
(20:14) Applied function composition problem (word problem)
(23:19) Solve for the inverse function in the applied word problem
(27:23) Simplify a difference quotient (to help with a definition of the derivative problem using limits in calculus)
(30:47) Quadratic function problem statement
(31:11) Find y-intercept
(31:37) Find x-intercepts with factoring
(33:06) Quadratic formula to find the roots of the quadratic function
(34:07) Complete the square, find vertex, and graph the quadratic function
(40:19) Restrict the domain and find an inverse function

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