Q: Given the function $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f$$?

$$ x \in \mathbb{R}, x \neq 2 $$

Question 1

A city park is circular with its center at $$(2, 3)$$ and a point on the circle at $$(5, 7). $$What is the equation of the circle?

Accepted Answer

$$ (x - 2)^2$ + (y - 3)^2$ = 25 $$

Question 2

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

Accepted Answer

$$ x \in \mathbb{R}, x 
eq 2 $$

Question 3

A company’s profit $$P is $$modeled by $$P(x) = 5x - 20$$, where $$x is $$the number of units sold. How many units must be sold for the company to break even?

Accepted Answer

$$ x = 4 $$

Question 4

Given points $$A(1,2)$$ and $$B(5,10)$$, what is the midpoint $$M of $$segment $$AB$$?

Accepted Answer

$$ (3, 6) $$

Question 5

Which of the following graphs fails the vertical line test?

Accepted Answer

A circle centered at $$(0,0)$$

Question 6

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

Accepted Answer

$$ 9 $$

Question 7

A line passes through $$(2, 3)$$ and $$(4, 7). $$What is its equation in slope-intercept form?

Accepted Answer

$$ y = 2x - 1 $$

Question 8

Given $$f(x) = x^2$ and g(x) = x + 1$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$ 2x + h $$

Question 9

A population grows according to $$P(t) = 1000 + 50t. $$What is the average rate of change from $$t = 2 to$$ $$t = 6$$?

Accepted Answer

$$ 50 $$

Question 10

Which transformation describes the graph of $$f(x) = (x - 3)^2$ + 2$$ compared to $$g(x) = x^2$?

Accepted Answer

Shift right 3 units and up 2 units

Question 11

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

Accepted Answer

$$ x^2$ + 2x $$

Question 12

A piecewise function is defined as $$f(x) = \begin{cases} x+2 & x \u003c 0 \ 2x & x \geq 0 \end{cases}. $$What is $$f(-3)$$?

Accepted Answer

$$ -1 $$

Question 13

Which of the following lines is perpendicular to $$y = 3x + 2$$?

Accepted Answer

$$ y = -\frac{1}{3}x + 4 $$

Question 14

Given the function $$f(x) = \sqrt{x-1}$$, what is the domain?

Accepted Answer

$$ x \geq 1 $$

Question 15

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

Accepted Answer

$$ 7 $$

Question 16

A function $$f is $$constant on the interval $$[2, 5]. $$Which of the following best describes its graph on this interval?

Accepted Answer

A horizontal line

Question 17

If $$f(x) = 3x - 2$$, what is the zero of $$f$$?

Accepted Answer

$$ x = \frac{2}{3} $$

Question 18

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

Accepted Answer

$$ x \in \mathbb{R} $$

Question 19

A car rental company charges a flat fee of $$20 plus 0.15 $$per mile driven. Write the equation for the total cost $$C$$ for $$m$$ miles driven.

Accepted Answer

$$ C = 0.15m + 20 $$

Question 20

Which transformation results in the graph of $$f(x) = -x^2$ from g(x$$) = $$x^2$$?

Accepted Answer

Reflection across the x-axis

College Algebra: Study Guide for Test 1 (Chapters 1 & 2)

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