Question 1

Which of the following describes the effect of the transformation $$f(x) \rightarrow f(x-3) + 2 on $$the parent function $$f(x)$$?

Accepted Answer

A shift 3 units to the right and 2 units up

Question 2

Given the function $$g(x) = -2f(x)$$, which transformation is applied to the parent function $$f(x)$$?

Accepted Answer

Reflection over the $$x-$$axis and vertical stretch by a factor of 2

Question 3

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 4

If $$h(x) = f(g(x))$$ and $$f(x) = x^2$, g(x) = x+1$, what is h(x$$)$$?

Accepted Answer

$$h(x) = (x+1)^2$

Question 5

Which statement is true about the symmetry of the function $$f(x) = \cos x$$?

Accepted Answer

It is even and symmetric about the $$y-$$axis

Question 6

What is the inverse of the function $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-5}{2}$$

Question 7

A function $$f(x) is $$reflected over the $$y-$$axis and then shifted 4 units up. Which equation represents this transformation?

Accepted Answer

$$f(-x) + 4$$

Question 8

Given $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = (\sqrt{x})^2$ = x$$

Question 9

Which of the following describes the domain and range of the parent function $$f(x) = \sqrt{x}$$?

Accepted Answer

Domain: $$[0, \infty)$$, Range: $$[0, \infty)$$

Question 10

If $$f(x) = x^2$ and g(x) = 3x$, what is the composite function f(g(x$$))$$?

Accepted Answer

$$f(g(x)) = (3x)^2$ = 9x^2$

Question 11

Which transformation results in a vertical compression of the parent function $$f(x) by a $$factor of $$\frac{1}{2}$$?

Accepted Answer

$$\frac{1}{2}f(x)$$

Question 12

If $$f(x) is $$odd, which of the following must be true for all $$x in $$the domain of $$f$$?

Accepted Answer

$$f(-x) = -f(x)$$

Question 13

Which of the following is the correct inverse of $$f(x) = \frac{1}{x}$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{1}{x}$$

Question 14

A real-world application: The height $$h (in $$meters) of a ball thrown upward is modeled by $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the parent function of $$h(t)$$?

Accepted Answer

$$f(x) = x^2$

Question 15

Which of the following is a reflection of $$f(x)$$ over the $$x-$$axis?

Accepted Answer

$$-f(x)$$

Question 16

If $$f(x) = x^2$ and g(x) = x+2$, what is f(g(x$$))$$?

Accepted Answer

$$f(g(x)) = (x+2)^2$

Question 17

Which of the following is the correct domain for the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

All real numbers except $$x = 3$$

Question 18

Which of the following complex numbers is in standard form?

Accepted Answer

$$3 + 2i$$

Question 19

If $$f(x) = x^2$ and g(x) = 2x$, what is (g$$ \circ f)(x)$$?

Accepted Answer

$$(g \circ f)(x) = 2x^2$

Trigonometry Study Guide: Functions, Transformations, Symmetry, and Complex Numbers

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