Question 1

Given the equation of a line passing through the points $$A(2, 3)$$ and $$B(6, 11)$$, what is the slope-intercept form of the line?

Accepted Answer

$$y = 2x - 1$$

Question 2

Which of the following is the domain of the function $$f(x) = \dfrac{1}{x-4}$$?

Accepted Answer

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

Question 3

A chemical reaction's rate $$R is $$modeled by $$R(t) = 5t^2$ - 3t + 2. $$What is the rate at $$t = 3$$ seconds?

Accepted Answer

$$38$$

Question 4

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x-4)(x-5)$$

Question 5

A medical dosage is modeled by $$D(x) = 2x^2$ + 5x - 3. $$For what value of $$x$$ does $$D(x) = 0$$?

Accepted Answer

$$x = \dfrac{-5 \pm \sqrt{25 + 24}}{4}$$

Question 6

Which of the following is NOT a solution to the inequality $$2x - 5 \u003c 7$$?

Accepted Answer

$$x = 7$$

Question 7

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

Accepted Answer

$$3$$

Question 8

A company’s profit $$P in $$thousands of dollars is given by $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit?

Accepted Answer

$$18$$

Question 9

Which of the following is the solution set for the equation $$|3x - 2| = 7$$?

Accepted Answer

$$\left\{3, -\dfrac{5}{3}\right\}$$

Question 10

Which of the following is the correct simplification of the rational expression $$\dfrac{x^2$ - 16}{x^2$ - 8x + 16}$$?

Accepted Answer

$$\dfrac{x+4}{x-4}$$

Question 11

A population of bacteria triples every hour. If the initial population is 200, which function models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 200 \cdot 3^t$$

Question 12

Which of the following is the solution to the system of equations: $$\begin{cases} x + y = 5 \ 2x - y = 4 \end{cases}$$?

Accepted Answer

$$(3, 2)$$

Question 13

If $$g(x) = \dfrac{2x+1}{x-3}$$, what is the value of $$g(4)$$?

Accepted Answer

$$9$$

Question 14

Which of the following is the correct solution to the quadratic equation $$x^2 + 6x + 5 = 0$?

Accepted Answer

$$x = -1, x = -5$$

Question 15

A projectile is launched from the ground and its height $$h in $$meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 19.6t. At $$what time does it reach its maximum height?

Accepted Answer

$$t = 2$$

Question 16

Which of the following is the correct solution to the inequality $$x^2 - 4x$$ \u003e 0$$?

Accepted Answer

$$(-\infty, 0) \cup (4, \infty)$$

Question 17

If $$f(x) = 3x - 7$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$5$$

Question 18

Which of the following is the correct factorization of $$6x^2 - 11x - 10$?

Accepted Answer

$$(2x + 5)(3x - 2)$$

Question 19

A car rental company charges a flat fee of $$\30$ plus $$\$$0.20$$ per mile driven. Which function models the total cost $$C$$ for $$m$$ miles?

Accepted Answer

$$C(m) = 0.20m + 30$$

Question 20

Which of the following is the solution to the equation $$\dfrac{2}{x} = 5$$?

Accepted Answer

$$x = \dfrac{2}{5}$$

Key Concepts in College Algebra: Functions, Equations, and Factoring

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