Question 1

Solve the inequality $$10x - 4x + 3 \u003c 3(x + 5)$$ and write the solution set in interval notation.

Accepted Answer

$$(-\infty, 4)$$

Question 2

Solve the compound inequality $$2x - 5 \u003c 3 \u003c 7$$ and write the solution set in interval notation.

Accepted Answer

$$(-4, 2)$$

Question 3

Solve the quadratic inequality $$x^2 - 4x - 12$$ \u003e 0$$ and write the solution set in interval notation.

Accepted Answer

$$(-\infty, -2) \cup (6, \infty)$$

Question 4

A company has a fixed cost of $$90,000 and a variable cost of 150$ per bicycle produced. Write the total cost function C(x$$)$$ and find C(110$$)$$. What does C(110$$)$ represent?

Accepted Answer

$$C(x) = 90,000 + 150x$$; $$C(110) = 106,500$$; It costs $$106,500 to $$produce $$110$$ bicycles.

Question 5

Find the slope of the line passing through the points $$(1, 3)$$ and $$(3, 7).$$

Accepted Answer

$$2$$

Question 6

Given the function $$f(x) = x^2$ - 4x + 1$$, evaluate $$f(-1).$$

Accepted Answer

$$6$$

Question 7

A car was purchased for $$22,500$$ and depreciates by $$3,300$$ per year for the first six years. Write a function $$V(x)$$ for the value after $$x$$ years and find $$V(2). $$What does $$V(2)$$ represent?

Accepted Answer

$$V(x) = 22,500 - 3,300x$$; $$V(2) = 15,900$$; The value of the car after $$2$$ years is $$15,900.$$

Question 8

Find the equation of the line passing through $$(6, 3)$$ with slope $$-2 in $$standard form.

Accepted Answer

$$2x + y = 15$$

Question 9

Determine whether the relation $$\{(4, 2), (5, 2), (4, 1)\}$$ defines a function.

Accepted Answer

No

Question 10

Find the average rate of change per year in the number of high school dropouts from $$1975$$ ($$5217$$ thousand) to $$2003$$ ($$3121$$ thousand).

Accepted Answer

$$-74.9$$ thousand per year; the number of dropouts decreased by an average of $$74.9$$ thousand each year from $$1975 to$$ $$2003$$

Question 11

Rewrite the equation $$3x + y - 4 = 0 in $$slope-intercept form and state the slope and y-intercept.

Accepted Answer

$$y = -3x + 4$$; slope $$-3$$, y-intercept $$4$$

Question 12

Given the function $$f(x) = \frac{5x^2$ - 1}{x^2$}$$, evaluate $$f(5).$$

Accepted Answer

$$\frac{124}{25}$$

Question 13

Find the slope of the line passing through $$(-7, 9)$$ and $$(5, 9)$$ and describe the line.

Accepted Answer

Slope $$0$$; the line is horizontal.

Question 14

Find the slope of the line passing through $$(-5, -1)$$ and $$(-5, 8)$$ and describe the line.

Accepted Answer

Slope undefined; the line is vertical.

Question 15

Given the linear function $$f(x) = -\frac{2}{3}x + 4$$, what are the slope and y-intercept?

Accepted Answer

Slope $$-\frac{2}{3}$$, y-intercept $$4$$

Question 16

Write the equation of the line passing through $$(-13, 15)$$ with undefined slope in standard form.

Accepted Answer

$$x = -13$$

Question 17

Determine whether the lines $$y = 3x - 7$$ and $$y = \frac{4}{5}x - 1$$ are parallel, perpendicular, or neither.

Accepted Answer

Neither

Question 18

Find the equation of the line passing through $$(2, -11)$$ with slope $$0 in $$standard form.

Accepted Answer

$$y = -11$$

Question 19

Given the function $$f(x) = x^2$ + 4x + 1$$, evaluate $$f(-x).$$

Accepted Answer

$$x^2 - 4x + 1$

College Algebra Test 2 Review: Step-by-Step Study Guidance

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