Q: A company’s profit $$P is $$modeled by the function $$P(x) = 3x - 7$$, where $$x is $$the number of units sold. What is the profit if 10 units are sold?

$$P(10) = 3 \times 10 - 7 = 23$$

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

$$(f \circ g)(3) = f(g(3)) = f(9) = 2 \times 9 + 1 = 19$$

Question 1

A pharmaceutical company needs to ensure that the concentration of a drug in a solution stays between 2 mg/mL and 5 mg/mL for safety. Which inequality correctly models the acceptable concentration $$c$$?

Accepted Answer

$$2 \u003c c \u003c 5$$

Question 2

A delivery drone travels from point $$A(2, 3) to $$point $$B(8, 15). $$What is the distance between these two points?

Accepted Answer

$$\sqrt{(8-2)^2$ + (15-3)^2$} = \sqrt{36 + 144} = \sqrt{180} \approx 13.42$$

Question 3

A circle is centered at $$(4, -2)$$ and passes through the point $$(7, 2). $$What is the equation of the circle?

Accepted Answer

$$(x-4)^2$$ + $$(y+2)^2 = 25$

Question 4

A company’s profit $$P is $$modeled by the function $$P(x) = 3x - 7$$, where $$x is $$the number of units sold. What is the profit if 10 units are sold?

Accepted Answer

$$P(10) = 3 	imes 10 - 7 = 23$$

Question 5

Which of the following is the parent function for quadratic equations?

Accepted Answer

$$f(x) = x^2$

Question 6

A piecewise function is defined as $$f(x) = \begin{cases} x+2 & x \u003c 0 \ 2x-1 & x \geq 0 \end{cases}. $$What is $$f(-3)$$?

Accepted Answer

$$f(-3) = -3 + 2 = -1$$

Question 7

The graph of $$f(x) = |x| is $$shifted 4 units to the right and 3 units up. What is the equation of the transformed function?

Accepted Answer

$$f(x) = |x-4| + 3$$

Question 8

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

Accepted Answer

$$(f \circ g)(3) = f(g(3)) = f(9) = 2 	imes 9 + 1 = 19$$

Question 9

Solve the quadratic equation $$x^2 - 5x + 6 = 0$.

Accepted Answer

$$x = 2, x = 3$$

Question 10

A medical lab uses the equation $$|x - 7| = 3 to $$determine acceptable temperature deviations from 7°C. What are the possible values for $$x$$?

Accepted Answer

$$x = 10 	ext{ or } x = 4$$

Question 11

Solve the rational equation $$\frac{2}{x} = 4$$ for $$x.$$

Accepted Answer

Question 12

Solve the radical equation $$\sqrt{x+5} = 4.$$

Accepted Answer

$$x = 11$$

Question 13

Which of the following equations is in quadratic form?

Accepted Answer

$$x^2 + 3x + 2 = 0$

Question 14

A line passes through $$(1, 2)$$ and $$(4, 8). $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = 2x$$

Question 15

A function $$f(x) is $$defined as $$f(x) = \begin{cases} x^2$ & x \u003c 2 \ 3x - 4 & x \geq 2 \end{cases}. $$What is $$f(2)$$?

Accepted Answer

$$f(2) = 3 	imes 2 - 4 = 2$$

Question 16

A circle has equation $$(x-3)^2$$ + $$(y+1)^2 = 16$. What is the radius?

Accepted Answer

$$4$$

Question 17

Which transformation will reflect the parent function $$f(x) = x^2$ over the x$-axis?

Accepted Answer

$$f(x) = -x^2$

Question 18

A student solves the equation $$|2x - 5| = 7. $$What are the solutions?

Accepted Answer

$$x = 6, x = -1$$

Question 19

A quadratic equation $$x^2 + 4x + 1 = 0$ is solved using the quadratic formula. What are the solutions?

Accepted Answer

$$x = \frac{-4 \pm \sqrt{16 - 4}}{2} = \frac{-4 \pm \sqrt{12}}{2} = \frac{-4 \pm 2\sqrt{3}}{2} = -2 \pm \sqrt{3}$$

College Algebra Study Guide: Inequalities, Functions, Graphs, and Equations

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