Precalculus Function Transformations

Functions PreCal Review

Part 1: NO CALCULATOR; Parent Functions and their transformations

• Know the parent function by the name, equation or graph and be able to give the other two pieces of information

• Know the domain and range of the parent function or the transformation function

• Know if/when a function increased or decreases for both the parent or transformation function

• Know if/where a function has asymptotes for parent and transformation function

Multiple Choice

What is the domain of f(x) = x³

• D: (-∞, ∞) R: (-∞, ∞)

• D: (-∞, 0). R: (0, ∞)

• D: (0, ∞). R: (-∞, 0)

• Domain and Range can not be determined

Multiple Choice

What is the name of the parent function with equation: f(x) = ∛x

• Quadratice

• Square Root

• Cubic Root

• Cube Root

Multiple Select

Which of the following function transformation indicates: y-axis reflection, vertical stretch by factor of 4, horizontal shift left 3 and vertical shift of down 6

• f(x) = - |4x +3| -6

• f(x) = 4|-x + 3| - 6

• f(x) =| -4x -3| -6

• f(x) = 4| -x -3| -6

• None of the above

Multiple Choice

Which of the answers below cube root transformation of the parent frunction

• None of these

Multiple Select

Which of the following are parent functions (check all that apply)

• None of these

Part 2: Calculators may be used

• Operations with functions with and without algebraic expressions

• Function Composition

• Writing the inverse of a function

• Verifying if two functions are inverses by graphing and by composition

• Giving the domain and range

• Transformations: Determining the equation of a graphed transformation, explaining how a function graph was transformed or explaining how a function was transformed from the equation

Open Ended

Write the equation for the transformation from blue to green

Multiple Choice

f(x) = -x

g(x) = 2x + 3

h(x) = x² - 1

k(x) = -(x)³

Find: h(-2)

• 3

• -3

• 5

• -5

• none of these

Multiple Choice

f(x) = -x

g(x) = 2x + 3

h(x) = x² - 1

k(x) = -(x)³

Find: g(k(x+1))

• g(k(x+1) = 2x⁴+ 8x³ + 6x²⁺x

• g(k(x+1) =2x⁴ - 8x³-6x²-x

• g(k(x+1) = -2x⁴ - 8x³-6x²-x

• g(k(x+1) = -x³+2x²-x

• none of these

Multiple Choice

f(x) = x - 2

g(x) = -x

h(x) = |x| +3

Find g(f(x))

• g(f(x)) = x + 2

• g(f(x)) x - 2

• g(f(x)) = -x + 2

• g(f(x)) = -x - 2

Multiple Choice

$$h\left(x\right)\ =\ -\frac{9}{2x\ +\ 3}$$  Find the inverse, if one exists

• $$h\left(x\right)=-\frac{18}{x-6}$$  

• $$h\left(x\right)=-\frac{18}{x}-6$$  

• $$h\left(x\right)\ =\ \frac{x}{-18}-6$$  

• $$h\left(x\right)=-\frac{9}{2x\ -\ 3}$$  

• No inverse

Open Ended

f(x) = 7x + 3

g(x) = x²

h(x) = -6x + 2

Find f(x) + h(x) - g(2)

Studying

Use all the study materials to study for the tests

Reminder if you would like one-to-few study session, there are time frames for Friday you can choose from:

7:45 - 8:15 (google meet)

9:00-9:30 in person, up to 3 people

9:30-10:00, up to 3 people

10:00-10:30, up to 3 people

10:30-11:30, up to 3 people

11:30 - 12:00, up to 3 people

** When you email, I would suggest selecting first choice, 2nd choice, 3rd choice study session times because first to email me, first scheduled**