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 horizontal shift 3 units to the right and a vertical shift 2 units up.

Question 2

Given the function $$g(x) = -2f(x)$$, which transformation(s) are 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 $$f(x) = x^2$, g(x) = x+1$, what is h(2$$)$$?

Accepted Answer

$$9$$

Question 5

Which of the following is the inverse of $$f(x) = 2x + 5$$?

Accepted Answer

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

Question 6

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 7

Which of the following statements is true about the domain and range of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

Domain: $$x \geq 2$$, Range: $$y \geq 0$$

Question 8

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 9

If $$f(x) = x^2$ and g(x) = 3x$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$36$$

Question 10

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

Accepted Answer

Question 11

A function $$f(x) is $$vertically stretched by a factor of 5 and reflected over the $$x-$$axis. Which equation represents this transformation?

Accepted Answer

$$-5f(x)$$

Question 12

Which of the following is the composite function $$(g \circ f)(x) if$$ $$f(x) = x+2$$ and $$g(x) = x^2$?

Accepted Answer

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

Question 13

Which of the following complex numbers is in standard form?

Accepted Answer

$$3 + 4i$$

Question 14

If $$z_1 = 2 + 3i$ and z_2$ = 1 - 2i$$, what is $$z_1$$ + $$z_2$$?

Accepted Answer

$$3 + i$$

Question 15

Which of the following describes the symmetry of the function $$f(x) = |x|$$?

Accepted Answer

Even symmetry about the $$y-$$axis.

Question 16

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is (f$$ \circ g)(4)$$?

Accepted Answer

$$4$$

Question 17

Which transformation is represented by $$f(x) \rightarrow f(x+5)$$?

Accepted Answer

A horizontal shift 5 units to the left.

Question 18

If $$f(x) = x^2$ and g(x) = 2x$, what is (g$$ \circ f)(3)$$?

Accepted Answer

$$18$$

Question 19

Which of the following is the correct domain for the function $$f(x) = \frac{1}{x-4}$$?

Accepted Answer

All real numbers except $$x = 4$$

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

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