Q: What is the domain of $$f(x) = \frac{1}{x+3}$$?

$$\{x \mid x \neq -3\} or$$ $$(-\infty, -3) \cup (-3, \infty)$$

Q: The time $$t it $$takes for a block of ice to melt varies inversely with the temperature $$T in $$the room. If $$t = 2$$ hours when $$T = 60$$^{\circ}$$F$$, how long would it take if $$T = 80$$^{\circ}$$F$$?

$$t = \frac{2 \times 60}{80} = 1.5$$ hours

Q: A bicycle company has $$1800 in fixed costs and 90 $$per bicycle. What is the cost to manufacture 14 bikes in a day?

$$C = 1800 + 90 \times 14 = 3060$$

Question 1

What is the distance between the points $$(-5, 10)$$ and $$(4, -2)$$? Use the distance formula.

Accepted Answer

$$\sqrt{(4 - (-5))^2$ + (-2 - 10)^2$} = \sqrt{9^2$ + (-12)^2$} = \sqrt{81 + 144} = \sqrt{225} = 15$$

Question 2

Given the segment $$\overline{AB}$$ with $$A(-3, 4)$$ and $$B(2, -3)$$, what is the midpoint of the segment?

Accepted Answer

$$(\frac{-3+2}{2}, \frac{4+(-3)}{2}) = (\frac{-1}{2}, \frac{1}{2})$$

Question 3

Find the slope and $$y-$$intercept of the line $$16y - 8x + 4 = 0.$$

Accepted Answer

Slope: $$2$$, $$y-$$intercept: $$-\frac{1}{4}$$

Question 4

Which of the following sets represents a function?

Accepted Answer

{$$(1,4), (2,4), (3,5), (4,9)$$}

Question 5

Simplify $$\sqrt{200}.$$

Accepted Answer

$$10\sqrt{2}$$

Question 6

Rationalize the denominator: $$\frac{2}{\sqrt{7}}.$$

Accepted Answer

$$\frac{2\sqrt{7}}{7}$$

Question 7

What is the domain of $$f(x) = \frac{1}{x+3}$$?

Accepted Answer

$$\{x \mid x 
eq -3\} or$$ $$(-\infty, -3) \cup (-3, \infty)$$

Question 8

Evaluate $$f(-2) if$$ $$f(x) = 2x^2$ - 1.$$

Accepted Answer

$$2(-2)^2 - 1 = 8 - 1 = 7$

Question 9

Given $$f(x) = x^3$ and g(x$$) = $$-x^3$$, what transformation maps $$f(x) to$$ $$g(x)$$?

Accepted Answer

Reflection over the $$x-$$axis

Question 10

The time $$t it $$takes for a block of ice to melt varies inversely with the temperature $$T in $$the room. If $$t = 2$$ hours when $$T = 60$$^{\circ}$$F$$, how long would it take if $$T = 80$$^{\circ}$$F$$?

Accepted Answer

$$t = \frac{2 	imes 60}{80} = 1.5$$ hours

Question 11

A bicycle company has $$1800 in fixed costs and 90 $$per bicycle. What is the cost to manufacture 14 bikes in a day?

Accepted Answer

$$C = 1800 + 90 	imes 14 = 3060$$

Question 12

Given the function $$h(x) = \sqrt{12x + 24}$$, what is its domain?

Accepted Answer

$$\{x \mid 12x + 24 \geq 0\} or$$ $$[-2, \infty)$$

Question 13

Which of the following best describes the transformation from $$f(x) = x^2$ to g(x$$) = $$(x-3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units

Question 14

If $$f(x) = x^3$ and g(x$$) = $$-x^3$$, which of the following statements is true?

Accepted Answer

$$g(x) is an $$odd function and is a reflection of $$f(x)$$ over the $$x-$$axis.

Question 15

Given $$f(x) = \sqrt{x}$$ and $$g(x) = \sqrt{2x}$$, what transformation maps $$f(x) to$$ $$g(x)$$?

Accepted Answer

Horizontal compression by a factor of $$\frac{1}{2}$$

Question 16

Find the average rate of change of $$f(x) = 2x^2$ - 1$$ from $$x = 1 to$$ $$x = 3.$$

Accepted Answer

$$\frac{f(3) - f(1)}{3 - 1} = \frac{17 - 1}{2} = 8$$

Question 17

Which of the following is the equation of the line perpendicular to $$3x - 9y = -9$$ and passing through $$(1,8)$$?

Accepted Answer

$$y - 8 = -\frac{1}{3}(x - 1)$$

Question 18

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

Accepted Answer

$$f(5) + g(5) = [2(25) - 1] + [5(5) + 2] = 49 + 27 = 76$$

College Algebra Unit 1 Review: Step-by-Step Guidance

Study Guide - Practice Questions

Study Guide - Flashcards