Question 1

A cell phone tower is located at point $$A(2, 3)$$ and a hospital is at point $$B(8, 15). $$What is the distance between the tower and the hospital, in units?

Accepted Answer

$$\sqrt{(8-2)^2$ + (15-3)^2$} = \sqrt{36 + 144} = \sqrt{180} = 6\sqrt{5}$$

Question 2

Given the equation $$x^2$$ + $$y^2 = 16$, which of the following statements is true about its symmetry?

Accepted Answer

It is symmetric with respect to the x-axis, y-axis, and the origin.

Question 3

Find the equation of the line passing through the points $$(-2, 5)$$ and $$(4, -1) in $$slope-intercept form.

Accepted Answer

$$y = -x + 3$$

Question 4

Which of the following relations is NOT a function?

Accepted Answer

$$\{(1,2), (2,3), (1,4)\}$$

Question 5

Let $$f(x) = \sqrt{x-2}. $$What is the domain of $$f$$?

Accepted Answer

$$[2, \infty)$$

Question 6

Suppose $$f(x) = 2x + 1$$ and $$g(x) = x^2$. What is (f$$ \circ g)(3)$$?

Accepted Answer

$$2 \cdot (3^2$) + 1 = 2 \cdot 9 + 1 = 19$$

Question 7

A company’s profit $$P$$ varies directly with the number of units $$x$$ sold. If $$P = 5000$$ when $$x = 250$$, what is the direct variation equation?

Accepted Answer

$$P = 20x$$

Question 8

Given $$f(x) = x^2$ - 4$$ and $$g(x) = x - 2$$, find the domain of $$\dfrac{f(x)}{g(x)}.$$

Accepted Answer

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

Question 9

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 10

A rectangle has a length that is 3 times its width. If the perimeter is 48 units, what is the area of the rectangle?

Accepted Answer

$$108$$

Question 11

Which of the following equations represents a line perpendicular to $$y = 2x + 5$$ and passing through $$(0, 1)$$?

Accepted Answer

$$y = -\dfrac{1}{2}x + 1$$

Question 12

Given the piecewise function $$f(x) = \begin{cases} x+2 & x \u003c 0 \ 3x & x \geq 0 \end{cases}$$, what is $$f(-3) + f(2)$$?

Accepted Answer

$$(-3+2) + (3 \cdot 2) = (-1) + 6 = 5$$

Question 13

Which of the following best describes the transformation from $$f(x) to$$ $$g(x) = f(x-4) + 2$$?

Accepted Answer

Shift right 4 units and up 2 units.

Question 14

If $$y$$ varies inversely as $$x$$ and $$y = 10$$ when $$x = 3$$, what is $$y$$ when $$x = 5$$?

Accepted Answer

$$y = 6$$

Question 15

Which of the following equations is the general form of a line passing through $$(1, -2)$$ with slope $$m = 4$$?

Accepted Answer

$$4x - y = 6$$

Question 16

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

Accepted Answer

$$(2^2) - (2 + 1) = 4 - 3 = 1$

Question 17

Which of the following best describes the graph of $$y = |x|$$?

Accepted Answer

A V-shaped graph opening upwards with vertex at the origin.

Question 18

A function $$f is $$defined by $$f(x) = \dfrac{1}{x-3}. $$Which of the following is true about its domain?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 19

Given the function $$f(x) = x^2$ - 6x + 8$$, for which values of $$x is$$ $$f(x) = 0$$?

Accepted Answer

$$x = 2$$ and $$x = 4$$

College Algebra Exam 1 Study Guide: Foundations and Functions

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