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

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

Question 1

Given the function $$f(x) = 2x^2$ - 3x + 5$$, what is $$f(4)$$?

Accepted Answer

$$f(4) = 2(4)^2$ - 3(4) + 5 = 32 - 12 + 5 = 25$$

Question 2

Which of the following relations is NOT a function?

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

$$\{y \in \mathbb{R} \mid y \geq 0\}$$

Question 5

A company’s profit function is $$P(x) = 5x - 20$$, where $$x is $$the number of units sold. What is the minimum number of units that must be sold for the company to break even?

Accepted Answer

$$x = 4$$

Question 6

Which of the following functions is linear?

Accepted Answer

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

Question 7

For the function $$f(x) = -2x + 7$$, over which interval is the function decreasing?

Accepted Answer

All real numbers $$x \in \mathbb{R}$$

Question 8

Write the equation of the line passing through $$(2, 5)$$ with slope $$m = -3 in $$point-slope form.

Accepted Answer

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

Question 9

Which of the following is the equation of a vertical line passing through $$(4, -2)$$?

Accepted Answer

$$x = 4$$

Question 10

A biologist models the population of bacteria as $$P(t) = 200 + 50t$$, where $$t is $$time in hours. What is the slope of the population growth, and what does it represent?

Accepted Answer

Slope is $$50$$, representing the rate of increase in bacteria per hour.

Question 11

Solve the equation $$2x - 5 = 9$$ and classify the solution.

Accepted Answer

Conditional; $$x = 7$$

Question 12

A student’s grade is calculated as $$G = 0.4x + 0.6y$$, where $$x is $$the midterm score and $$y is $$the final exam score. If the student scored $$x = 80$$ and $$y = 90$$, what is their grade?

Accepted Answer

$$G = 0.4(80) + 0.6(90) = 32 + 54 = 86$$

Question 13

Solve the inequality $$3x - 7 \u003c 2$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, 3)$$

Question 14

Which of the following is the correct graph for the piecewise function $$f(x) = \begin{cases} x+2 & x \u003c 0 \ 3 & x \geq 0 \end{cases}$$?

Accepted Answer

A line with slope 1 for $$x \u003c 0$$ and a constant value 3 for $$x \geq 0$$

Question 15

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

Accepted Answer

$$C = 0.15m + 20$$

Question 16

If $$y$$ varies directly with $$x$$ and $$y = 12$$ when $$x = 3$$, what is the equation relating $$y$$ and $$x$$?

Accepted Answer

$$y = 4x$$

Question 17

Given the function $$f(x) = x^2$ - 4x + 3$$, find the $$x-$$intercepts.

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 18

A medication’s concentration in the bloodstream is modeled by $$C(t) = 10 - 2t$$, where $$t is $$hours after administration. After how many hours will the concentration reach zero?

Accepted Answer

$$t = 5$$

Question 19

For the function $$f(x) = x^2$ - 6x + 9$$, determine the interval where the function is decreasing.

Accepted Answer

$$(-\infty, 3)$$

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

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