Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x + 4}$$?

Accepted Answer

$$[-4, \infty)$$

Question 2

Given the points $$A(-2, 2)$$ and $$B(3, -6)$$, what is the distance between them?

Accepted Answer

$$\sqrt{89}$$

Question 3

Which of the following equations represents a circle with center $$(3, -7)$$ and radius $$5$$?

Accepted Answer

$$(x - 3)^2$ + (y + 7)^2$ = 25$$

Question 4

If $$f(x) = x^2$ - 5$$, which of the following statements is true about $$f$$?

Accepted Answer

$$f is an $$even function

Question 5

A function $$f is $$defined as $$f(x) = 2x + 3. $$What is the average rate of change of $$f$$ from $$x = 1 to$$ $$x = 4$$?

Accepted Answer

$$2$$

Question 6

Which of the following is the correct difference quotient for $$f(x) = x^2$?

Accepted Answer

$$\dfrac{(x+h)^2$ - x^2$}{h}$$

Question 7

Suppose $$y$$ varies inversely as $$x. If$$ $$y = 8$$ when $$x = 2$$, what is the equation relating $$y$$ and $$x$$?

Accepted Answer

$$y = \dfrac{16}{x}$$

Question 8

Which of the following is the equation of the line passing through $$(2, -3)$$ and parallel to $$2x + 5y = 20$$?

Accepted Answer

$$y = -\dfrac{2}{5}x - \dfrac{4}{5}$$

Question 9

Given $$f(x) = x^2$ - 7$$ and $$g(x) = -6x + 5$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(-6x + 5)^2$ - 7$$

Question 10

A piecewise function is defined as $$f(x) = \begin{cases} -2x^2$ & x \u003c -3 \ \sqrt{8 + 2x} & -3 \leq x \u003c 4 \ |4 - 2x| & x \geq 4 \end{cases}. $$What is $$f(6)$$?

Accepted Answer

$$|4 - 2 \cdot 6| = 16$$

Question 11

Which of the following transformations will shift the graph of $$y = f(x) up by 3 $$units?

Accepted Answer

$$y = f(x) + 3$$

Question 12

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

Accepted Answer

$$f is an $$odd function

Question 13

A community college has 30 ft of dividers to form two sides of a rectangular testing center in a corner. If $$x is $$the length, what function models the area $$A(x)$$?

Accepted Answer

$$A(x) = x(30 - x)$$

Question 14

Which of the following is the correct equation for a line perpendicular to $$y = \frac{1}{2}x + 3$$ and passing through $$(0, 1)$$?

Accepted Answer

$$y = -2x + 1$$

Question 15

If $$f(x) = \frac{1}{x - 3}$$, which value is NOT in the domain of $$f$$?

Accepted Answer

$$x = 3$$

Question 16

Which of the following best describes the range of the greatest integer function $$f(x) = \lfloor x \rfloor$$?

Accepted Answer

All integers

Question 17

If $$y$$ varies jointly as $$x$$ and $$z$$, and $$y = 42$$ when $$x = 2$$ and $$z = 3$$, what is the equation relating $$y$$, $$x$$, and $$z$$?

Accepted Answer

$$y = 7xz$$

Question 18

Which of the following is the correct composition $$(g \circ f)(x) if$$ $$f(x) = x^2$ and g(x) = x + 1$?

Accepted Answer

$$g(f(x)) = x^2$ + 1$$

Question 19

Which of the following is the correct equation for a vertical line passing through $$(2, -3)$$?

Accepted Answer

$$x = 2$$

College Algebra: Graphs, Functions, and Models – Study Notes

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