Question 1

Given the graph in Image 1, which of the following statements is true about the function's local extrema?

Accepted Answer

The function has a local maximum at $$x \approx -2$$ and a local minimum at $$x \approx 4.$$

Question 2

For the function shown in Image 2, which of the following intervals is the function increasing?

Accepted Answer

The function is increasing on $$(2, \infty)$$ and $$(-\infty, -2).$$

Question 3

In Image 3, the function $$f(x)$$ has a vertical asymptote. At which $$x-$$value does this occur?

Accepted Answer

$$x = 0$$

Question 4

Based on the graph in Image 4, what is the end behavior of the function as $$x 	o \infty$$?

Accepted Answer

The function approaches $$y = \infty.$$

Question 5

In Image 5, which of the following best describes the concavity of the function on the interval $$(-\infty, 0)$$?

Accepted Answer

The function is concave down on $$(-\infty, 0).$$

Question 6

For the function in Image 6, what is the $$y-$$intercept?

Accepted Answer

$$y = 0$$

Question 7

Which of the following best describes the symmetry of the function in Image 7?

Accepted Answer

The function is even.

Question 8

Suppose the function in Image 1 models the height (in meters) of a projectile over time (in seconds). At what time does the projectile reach its maximum height?

Accepted Answer

At $$x \approx -2$$ seconds.

Question 9

Given the function in Image 3, which of the following statements about its domain is correct?

Accepted Answer

The domain is all real numbers except $$x = 0.$$

Question 10

For the function in Image 6, which of the following best describes its behavior as $$x 	o -\infty$$?

Accepted Answer

The function approaches $$y = -1.$$

Question 11

Which of the following graphs (from the images) most likely represents a cubic function?

Accepted Answer

Image 1

Question 12

In Image 2, what is the nature of the critical point at $$x = 0$$?

Accepted Answer

It is a point of inflection.

Question 13

For the function in Image 4, which of the following best describes the concavity at $$x = 0$$?

Accepted Answer

The function is concave down at $$x = 0.$$

Question 14

Which image shows a function with a horizontal asymptote at $$y = 1$$?

Accepted Answer

Image 6

Question 15

In Image 5, what happens to the function as $$x$$ approaches $$0$$ from the left?

Accepted Answer

The function approaches $$-\infty.$$

Question 16

Which of the following best describes the function in Image 7?

Accepted Answer

It is a parabola opening upwards.

Comprehensive Calculus II Exam Review: Derivatives, Curve Sketching, and Analysis

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