Question 1

Which of the following points is located in Quadrant II of the rectangular coordinate system?

Accepted Answer

$$(-2, 3)$$

Question 2

Given the equation $$y = 2x - 5$$, what is the $$y-$$intercept of the graph?

Accepted Answer

$$(0, -5)$$

Question 3

What is the slope of the line passing through the points $$(1, 2)$$ and $$(4, 8)$$?

Accepted Answer

$$m = \frac{8-2}{4-1} = 2$$

Question 4

Which equation represents a line parallel to $$y = -3x + 2$$?

Accepted Answer

$$y = -3x - 4$$

Question 5

What is the domain of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$[2, \infty)$$

Question 6

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

Accepted Answer

$$x^2 + x + 1$

Question 7

Which transformation results in the graph of $$f(x)$$ being reflected over the $$x-$$axis?

Accepted Answer

$$-f(x)$$

Question 8

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

Accepted Answer

$$[0, \infty)$$

Question 9

Which of the following is NOT a function?

Accepted Answer

$$x^2$$ + $$y^2 = 25$

Question 10

Given $$f(x) = x^2$ + 3x - 10$$, express $$f(x) as a $$composition $$f(x) = (h \circ k)(x)$$ for some functions $$h$$ and $$k.$$

Accepted Answer

$$h(x) = x - 10,\ k(x) = x^2$ + 3x$$

Question 11

What is the equation of the line in point-slope form that passes through $$(2, -4)$$ with a slope of $$0$$?

Accepted Answer

$$y + 4 = 0(x - 2)$$

Question 12

If $$f(x) = x^2$ and g(x) = x - 1$, what is (f$$ \circ g)(3)$$?

Accepted Answer

$$f(g(3)) = f(2) = 4$$

Question 13

Which of the following describes a vertical shift of the function $$f(x) up by$$ $$3$$ units?

Accepted Answer

$$f(x) + 3$$

Question 14

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

Accepted Answer

$$(-\infty, 5) \cup (5, \infty)$$

Question 15

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

Accepted Answer

$$[-4, 5)$$

Question 16

If $$f(x) = |x|$$, which transformation results in $$g(x) = |x - 3| + 2$$?

Accepted Answer

Shift $$f(x)$$ right by $$3$$ units and up by $$2$$ units

Question 17

Given $$f(x) = x^2$ and g(x$$) = \sqrt{x-8}$$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$[8, \infty)$$

Question 18

Which of the following best describes the effect of multiplying a function $$f(x) by a $$constant $$c \u003e 1$$?

Accepted Answer

The graph of $$f(x) is $$stretched vertically

Question 19

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

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Precalculus Study Notes: Functions and Graphs (Blitzer, Ch. 1)

Study Guide - Practice Questions