Question 1

Which of the following best describes the relationship between the three graphs shown in the first image (top left, labeled [−2.35, 2.35] by [−1.5, 1.5])?

Accepted Answer

They are all power functions with the same intercepts but different rates of increase.

Question 2

In the second and third images (labeled [−5, 5] by [−15, 15] and [−20, 20] by [−200, 200]), the graphs show a family of functions with a vertical asymptote. Which type of function is most likely being graphed?

Accepted Answer

Rational functions

Question 3

The graphs in the fourth, fifth, and sixth images ([−1.5, 1.5] by [−0.5, 1.5], [−5, 5] by [−5, 25], [−15, 15] by [−50, 400]) all have the same general shape but different vertical stretches. What transformation is being applied to the base function?

Accepted Answer

Vertical stretch/shrink

Question 4

Given the graph in the seventh image (line through (−2, 4) and (3, 1)), what is the equation of the line in slope-intercept form?

Accepted Answer

$$y = -\frac{3}{5}x + 2.8$$

Question 5

The eighth image shows a line passing through (1, 5) and (−2, −3). What is the slope of this line?

Accepted Answer

$$\frac{8}{3}$$

Question 6

The ninth image ([−5, 5] by [−20, 20]) shows a function with a vertical asymptote and a decreasing branch on the left. Which of the following is a possible equation for this function?

Accepted Answer

$$y = \frac{1}{x}$$

Question 7

The tenth image ([−5, 5] by [−19, 1]) shows a function with a vertical asymptote and the graph approaches negative infinity as $$x$$ approaches 0 from the right. Which function best matches this behavior?

Accepted Answer

$$y = -\frac{1}{x^2$}$$

Question 8

The eleventh image ([−5, 5] by [−1, 49]) shows a function with a minimum at the origin and increasing rapidly for large $$|x|. $$Which function is most likely being graphed?

Accepted Answer

$$y = x^4$

Question 9

The twelfth image ([−5, 5] by [−50, 50]) shows a function with a vertical asymptote and the graph increases without bound as $$x$$ increases. Which function best matches this behavior?

Accepted Answer

$$y = \frac{1}{x^3$}$$

Question 10

The thirteenth image shows a line passing through (2, 4) and (−5, −1). What is the equation of the line in point-slope form using the point (2, 4)?

Accepted Answer

$$y - 4 = \frac{5}{7}(x - 2)$$

Question 11

The fourteenth image shows a line passing through (−3, 5) and (6, −2). What is the slope of this line?

Accepted Answer

$$-\frac{7}{9}$$

Question 12

The fifteenth image shows a line passing through (−4, 6) and (−1, 2). What is the y-intercept of this line?

Accepted Answer

$$y = 10/3$$

Question 13

The sixteenth image shows a line passing through (1, 2) and (5, 7). What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = \frac{5}{4}x - \frac{1}{4}$$

Question 14

The seventeenth image shows a line passing through (0, 3) and (3, 0). What is the slope of this line?

Accepted Answer

$$-1$$

Question 15

The eighteenth image shows a line passing through (−4, 0) and (0, 2). What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = -0.5x + 2$$

Polynomial and Rational Functions: Graphs, Properties, and Modeling

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