Question 1

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$$\{(1,2), (3,4), (5,5)\}$$

Question 2

Given the points $$(-1,3)$$ and $$(3,4)$$, what is the slope of the line passing through them, and does the line rise, fall, is horizontal, or vertical?

Accepted Answer

Slope is $$\frac{1}{4}$$; the line rises.

Question 3

Given the equation of a line passing through $$(3,5)$$ with a slope of $$2$$, what is the equation in point-slope form?

Accepted Answer

$$y - 5 = 2(x - 3)$$

Question 4

A line passes through $$(2, -3)$$ and is perpendicular to the line $$y = \frac{1}{5}x + 6. $$What is the slope of the required line?

Accepted Answer

$$-5$$

Question 5

Given $$f(x) = x^3$, which of the following describes the domain and range of f$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, \infty)$$

Question 6

What is the distance between the points $$(-2, -6)$$ and $$(3, -4)$$?

Accepted Answer

$$\sqrt{29}$$

Question 7

Find the midpoint of the segment with endpoints $$(10, 4)$$ and $$(2, 6).$$

Accepted Answer

$$(6, 5)$$

Question 8

Which of the following is the correct inverse of $$f(x) = 2x + 3$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-3}{2}$$

Question 9

Given the circle $$(x-4)^2$$ + $$(y-1)^2 = 16$, what is the center and radius?

Accepted Answer

Center: $$(4,1)$$, Radius: $$4$$

Question 10

What is the domain of $$f(x) = \frac{3}{x-4}$$?

Accepted Answer

$$(-\infty, 4) \cup (4, \infty)$$

Question 11

Which transformation is applied to $$f(x) = |x| to $$obtain $$g(x) = -2(|x+2|^2) + 1$$?

Accepted Answer

Shift left 2, vertical stretch by 2, reflect over x-axis, square, shift up 1

Question 12

Given $$f(x) = 3x + 8$$ and $$g(x) = \frac{x-8}{3}$$, are $$f$$ and $$g$$ inverses of each other?

Accepted Answer

Yes, because $$f(g(x)) = x$$ and $$g(f(x)) = x$$

Question 13

Evaluate $$f(-3)$$ for $$f(x) = \begin{cases} x-1 & x \u003c 0 \ 7x+3 & x \geq 0 \end{cases}$$

Accepted Answer

$$-4$$

Question 14

A medical researcher is tracking the spread of a virus. The number of cases $$C is $$modeled by $$C(t) = 5t + 9$$, where $$t is $$the number of days since the outbreak. What is the inverse function, and what does it represent?

Accepted Answer

$$C^{-1}(x$$) = \frac{x-9}{5}$$; it gives the number of days since the outbreak for a given number of cases.

Question 15

Which of the following best describes the range of the function $$f(x) = \sqrt{24 - 3x}$$?

Accepted Answer

$$[0, \sqrt{24}]$$

Question 16

A city plans to build a circular park with equation $$(x-5)^2$$ + $$(y+2)^2 = 49$. What is the center and radius of the park?

Accepted Answer

Center: $$(5, -2)$$, Radius: $$7$$

Question 17

Given the function $$g(x) = \begin{cases} x+3 & x \geq -3 \ -(x+3) & x \u003c -3 \end{cases}$$, what is $$g(-6)$$?

Accepted Answer

$$3$$

Question 18

A biologist measures the distance between two points on a petri dish: $$(4,1)$$ and $$(6,3). $$What is the distance?

Accepted Answer

$$2\sqrt{2}$$

Question 19

Which of the following is the correct midpoint of the segment with endpoints $$(-4,7)$$ and $$(1,-3)$$?

Accepted Answer

$$\left(-\frac{3}{2}, 2\right)$$

Question 20

Given $$f(x) = 5x - 9$$ and $$g(x) = \frac{x+5}{9}$$, are $$f$$ and $$g$$ inverses of each other?

Accepted Answer

No, because $$f(g(x)) 
eq x$$

College Algebra: Functions, Lines, and Graphs Study Guide

Guida di studio - Domande di pratica

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