Question 1

What is the distance between the points $$(2, -4)$$ and $$(5, 1)$$? Express your answer in the form $$\sqrt{N}$$, where $$N is a $$whole number.

Accepted Answer

$$\sqrt{29}$$

Question 2

Find the midpoint of the segment with endpoints $$\left(4, \frac{10}{7}\right)$$ and $$\left(-7, -\frac{2}{5}\right). $$Express your answer as $$\left(a, b\right).$$

Accepted Answer

$$\left(\frac{-3}{2}, \frac{44}{35}\right)$$

Question 3

Is the point $$\left(\frac{3}{2}, \frac{4}{3}\right) a $$solution to the equation $$8x - 6y = 5$$?

Accepted Answer

No, because substituting the values does not satisfy the equation.

Question 4

Which of the following sets represents a function? Explain.

Accepted Answer

$$\{(0, 4), (-1, 6), (1, 6), (2, 6), (-2, 3), (2, 5)\}$$, because some $$x-$$values are paired with more than one $$y-$$value.

Question 5

Given the equation $$2x - 4y = 8$$, what is the $$y-$$intercept of the line?

Accepted Answer

$$(0, 2)$$

Question 6

What is the slope of the line passing through the points $$(2, 6)$$ and $$(-8, -2)$$?

Accepted Answer

Question 7

Determine the slope and $$y-$$intercept of the line $$7x - 3y = 5.$$

Accepted Answer

Slope: $$\frac{7}{3}$$, $$y-$$intercept: $$(0, -\frac{5}{3})$$

Question 8

What is the domain of the function $$f(x) = x + 5$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 9

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

Accepted Answer

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

Question 10

Evaluate $$f(6)$$ for $$f(x) = \frac{x}{x-3}.$$

Accepted Answer

$$2$$

Question 11

Which of the following relations is a function?

Accepted Answer

A relation where each $$x-$$value is paired with exactly one $$y-$$value.

Question 12

Given the function $$f(x) = \frac{x}{x-3}$$, what is $$f\left(\frac{1}{2}\right)$$?

Accepted Answer

$$\frac{1}{2} / (\frac{1}{2} - 3) = -\frac{1}{5}$$

Question 13

Which of the following equations represents a vertical line?

Accepted Answer

$$x = 9$$

Question 14

A medical researcher is tracking the temperature of a patient every hour. Which of the following best describes the relationship between time (hours) and temperature (degrees) if each hour has only one temperature reading?

Accepted Answer

It is a function because each hour corresponds to exactly one temperature.

Question 15

Given the function $$f(x) = \frac{x}{x-3}$$, what is $$f(3)$$?

Accepted Answer

Undefined

Question 16

Which of the following best describes the range of a function whose graph is a horizontal line at $$y = 4$$?

Accepted Answer

$$\{4\}$$

Question 17

A chemical reaction's rate $$r (in $$mol/s) is measured at different temperatures $$T (in$$ $$^\circC). If $$each temperature yields only one rate, but some rates repeat, is the relation a function from $$T to$$ $$r$$?

Accepted Answer

Yes, because each temperature has only one rate.

Question 18

Which of the following is the correct formula for the distance between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 19

If a function $$f is $$defined by the set of points $$\{(1, 3), (2, 3), (3, 7), (4, 3), (5, 7), (6, 7), (6, 3), (8, 7)\}$$, is this a function?

Accepted Answer

No, because the $$x-$$value 6 is paired with more than one $$y-$$value.

College Algebra Exam 1 Practice – Step-by-Step Guidance

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