1.1 MathXL

• There is a zero at x = 4 because the function is changing from positive to negative at x = 4

• The function is positive at x = 4 because it is negative over the interval (4, ∞)

• There is a zero at x = 4 because the function is changing from negative to positive at x = 4

• The function is negative at x = 4 because it is positive over the interval (-∞, 4).

Describe and correct the error a student made in finding the interval(s) over which the function is positive and negative.

• The zeros are both positive and negative. The student included these in the interval over which the function is positive but not in which the function is negative, which is incorrect.

• The zeros are negative. The student included these in the interval over which the function is positive, which is incorrect.

• The zeros are neither positive nor negative. The student included these in the interval over which the function is positive, which is incorrect.

• The zeros are neither positive nor negative. The student included these in the interval over which the function is negative, which is incorrect.

Find the correct interval(s) over which the function is positive. (Type your answer in interval notation. Use a comma to separate answers as needed.)

• (-∞, -1)

• (3, ∞)

• (-∞, -1)

• (-1, 3)

Find the correct interval(s) over which the function is negative. (Type your answer in interval notation. Use a comma to separate answers as needed.)

• (-∞,-1) and (3,∞)

• (-∞, -1)

• (-1, 3)

• (3,∞)

Sketch a graph given the following key features:

• 
• 
• 
• 

A student says that all linear functions are either increasing or decreasing. Do you agree? Explain. Choose the correct answer below.

• Yes. Linear functions always have (-∞,∞) as their domain and range, so they are always increasing or always decreasing.

• No. Linear functions can be both increasing and decreasing.

• Yes. Linear functions always have an x- and y-intercept, so they are always increasing or decreasing.

• No. Linear functions can also be constant, which means neither increasing nor decreasing.

A relative maximum of a function occurs at the highest point on a graph over a certain interval. A relative minimum of a function occurs at the lowest point on a graph over a certain interval. Explain how to identify a relative maximum and a relative minimum of a function using key features. A relative maximum occurs when a function changes from _______ to _______. A relative minimum occurs when a function changes from _______ to _______.

• A relative maximum occurs when a function changes from increasing to decreasing.

• A relative minimum occurs when a function changes from decreasing to increasing.

• A relative maximum occurs when a function changes from decreasing to increasing.

• A relative minimum occurs when a function changes from increasing to decreasing.

• A relative maximum occurs when a function changes from constant to increasing.

For a graph of speed in miles per hour as a function of time in hours, what does it mean when the function is increasing? Decreasing? When the graph is increasing, the speed is _______. When the graph is decreasing, the speed is _______.

• When the graph is increasing, the speed is increasing.

• When the graph is decreasing, the speed is decreasing.

• When the graph is increasing, the speed is constant.

• When the graph is decreasing, the speed is constant.

• When the graph is increasing, the speed is decreasing.