$$(f \circ g)(x) = (\sqrt{x-8})^2$ = x-8$$, \text{ domain: } [8, \infty)$

Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each input has at most one output.

Question 2

Given the relation $$\{(-3, 5), (0, 2), (3, 5)\}$$, what are the inputs and outputs, and is this a function?

Accepted Answer

Inputs: $$\{-3, 0, 3\}$$, Outputs: $$\{5, 2\}$$, Yes, it is a function.

Question 3

Which equation represents a function?

Accepted Answer

$$y + 4 = 3x$$

Question 4

What is the domain of the function $$f(x) = \sqrt{x+4}$$?

Accepted Answer

$$[-4, \infty)$$

Question 5

Given $$f(x) = \frac{1}{x^2$-5x+6}$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, 2) \cup (2, 3) \cup (3, \infty)$$

Question 6

Which transformation results in a reflection of $$f(x)$$ over the x-axis?

Accepted Answer

$$-f(x)$$

Question 7

If $$f(x) = x^2$, what is the equation for the function g(x$$)$$ that is f(x$$)$$ shifted right by 3 and up by 2?

Accepted Answer

$$g(x) = (x-3)^2$ + 2$$

Question 8

Given $$f(x) = x^3$, write the equation for h(x$$)$$ if f(x$$)$$ is reflected over the x-axis and then shifted down 2 units.

Accepted Answer

$$h(x) = -x^3$ - 2$$

Question 9

Which of the following is the correct standard form equation for a circle with center $$(1, -2)$$ and radius $$3$$?

Accepted Answer

$$(x-1)^2$$ + $$(y+2)^2 = 9$

Question 10

Given $$f(x) = x^2$ and g(x$$) = \sqrt{x-8}$$, find (f$$ \circ g)(x)$$ and its domain.

Accepted Answer

$$(f \circ g)(x) = (\sqrt{x-8})^2$ = x-8$$, 	ext{ domain: } [8, \infty)$

Question 11

Which of the following is NOT a function?

Accepted Answer

$$x^2$$ + $$y^2 = 9$

Question 12

If $$f(x) = x^2$ + 4$$ and $$g(x) = 5x + 7$$, what is $$(f+g)(x)$$?

Accepted Answer

$$x^2 + 5x + 11$

Question 13

Given $$f(x) = \sqrt{x}$$ and $$g(x) = 3x - 6$$, what is the domain of $$(f \cdot g)(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 14

Which transformation will shift the graph of $$f(x)$$ left by 2 units and up by 3 units?

Accepted Answer

$$f(x+2) + 3$$

Question 15

What is the result of composing $$f(x) = \frac{1}{x^2$-2}$$ and $$g(x) = \sqrt{x+2} as$$ $$(f \circ g)(x)$$?

Accepted Answer

$$\frac{1}{(\sqrt{x+2})^2$-2}$$

Question 16

Given the general form $$x^2$$ + $$y^2 + 2x + 6y + 8 = 0$, what is the center and radius of the circle in standard form?

Accepted Answer

Center: $$(-1, -3)$$, Radius: $$\sqrt{2}$$

Question 17

Which of the following is the correct interval notation for the domain $$\{x | -4 \leq x \u003c 5\}$$?

Accepted Answer

$$[-4, 5)$$

Question 18

If $$f(x) = x^2$ + x + 2$$ and $$h(x) = x + \sqrt{x-8}$$, what is the domain of $$(f-h)(x)$$?

Accepted Answer

$$[8, \infty)$$

Functions and Their Graphs: Foundations, Transformations, and Circles

Study Guide - Practice Questions