Question 1

Solve the linear equation: $$11 - (x + 3) = 7(3x + 9).$$

Accepted Answer

$$x = 1.5$$

Question 2

Solve the compound inequality and write the answer in interval notation: $$-1 \u003c 3x - 2 \leq 7.$$

Accepted Answer

$$\left(\frac{1}{3}, 3\right]$$

Question 3

Solve the absolute value inequality $$|3x + 4| \u003c 10$$ and write the answer in interval notation.

Accepted Answer

$$(-\frac{14}{3}, 2)$$

Question 4

Find the distance between the points $$(-2, -1)$$ and $$(3, 11). $$Use the distance formula.

Accepted Answer

$$\sqrt{130}$$

Question 5

Find the slope of the line passing through $$(-4, 2)$$ and $$(3, 6).$$

Accepted Answer

$$\frac{4}{7}$$

Question 6

Given the equation $$y = \frac{2}{3}x - 4$$, what is the domain and range?

Accepted Answer

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

Question 7

Find the equation of the line in slope-intercept form that passes through $$(-1, 5)$$ and $$(2, -1).$$

Accepted Answer

$$y = -2x + 3$$

Question 8

What is the equation of the vertical line passing through $$(4, -7)$$? What is its slope?

Accepted Answer

Equation: $$x = 4$$, Slope: undefined

Question 9

Which of the following relations is a function? $$\{(3, -1), (-2,4), (0,8), (4, -1)\}$$

Accepted Answer

Yes, it is a function because each $$x-$$value is unique.

Question 10

Given $$f(x) = x^2$ - 4x$$ and $$g(x) = 2x - 5$$, find $$g(a+1).$$

Accepted Answer

$$2a - 3$$

Question 11

Given the piecewise function $$f(x) = \begin{cases} 3x-2, & x \leq -1 \ x^2$+1, & x \u003e -1 \end{cases}$$, find $$f(-2).$$

Accepted Answer

$$-4$$

Question 12

Let $$f(x) = 3x + 9$$, $$g(x) = x^2$ - 5$$, and $$h(x) = x + 2. $$Find $$(f \circ g)(x).$$

Accepted Answer

$$3(x^2 - 5) + 9$

Question 13

Find the difference quotient for $$f(x) = x + 3.$$

Accepted Answer

$$1$$

Question 14

A chemical reaction's temperature $$T (in$$ $$^\circC) is $$modeled by $$T = 2t + 5$$, where $$t is $$time in minutes. What is the temperature after 10 minutes?

Accepted Answer

$$T = 25$$

Question 15

Solve the inequality $$2x - 3 \u003c -11 or$$ $$-3x + 1 \leq -14.$$

Accepted Answer

$$x \u003c -4 or$$ $$x \geq 5$$

Question 16

Which of the following best describes the range of the function shown in the first image (parabola opening upward, vertex at $$(0, -5)$$, endpoints at $$(-4, 0)$$ and $$(4, 0)$$)?

Accepted Answer

$$[-5, 0]$$

Question 17

Given the graph in the first image, what is the domain of the function?

Accepted Answer

$$[-4, 4]$$

Question 18

If a line is perpendicular to $$x - 3y = 9$$, what is its slope?

Accepted Answer

$$\frac{1}{3}$$

Question 19

A medical dosage is modeled by $$D = 5t - 2$$, where $$D is $$the dosage in mg and $$t is $$time in hours. What is the dosage after 3 hours?

Accepted Answer

$$13 mg$$

Question 20

Find the equation of the line parallel to $$y = -\frac{1}{3}x + 7$$ that passes through $$(6, -4).$$

Accepted Answer

$$y = -\frac{1}{3}x - 2$$

College Algebra Midterm Review: Linear Equations, Inequalities, & Functions

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