Algebra Comparing Functions

Function A is represented by the equation y = 4x - 2. Function B is represented by the table.
Which of these functions has the greater rate of change?

• Function A. It's rate of change is -2.

• Function A. It's rate of change is 4.

• Function B. It's rate of change is 2.

• Function B. It's rate of change is 6.

Janet is planning her sweet sixteen birthday party. She must decide which party coordinator she should use so that she spends the least amount of money possible. Each coordinator charges an initial fee for their services, plus an additional fee depending on the number of guests that attend the party. Each coordinator's rates are shown in the image. Which coordinator charges the greatest fee per guest?

• Coordinator A

• Coordinator B

• Coordinator C

• Coordinator D

Jasmine compared the x-intercept of f(x) = 2x – 8 to the x-intercept of the function shown in the table.

What is the value of the larger x-intercept of the two functions?

• -8

• -2

• 4

• 16

Which function has a greater rate of change than the function A in the table?

• F
• G
• H
• J

• A

• B

• C

• D

• E

The graph of f(x) = x² is shown on the grid. Which statement about the relationship between the graph of f and teh graph of g(x) = 7x² is true?

• The graph of g is narrower than the graph of f.

• The graph of g is wider than the graph of f.

• The graph of g is 7 units below the graph of f.

• The graph of g is 7 units above the graph of f.

Which statement compares the graphs of f(x) and g(x) over the interval [0, 5]?

• The graph of f(x) always exceeds the graph of g(x) over the interval [0, 5].

• The graph of g(x) always exceeds the graph of f(x) over the interval [0, 5].

• The graph of g(x) exceeds the graph of f(x) over the interval [0, 4], the graphs intersect at a point between 4 and 5, and then the graph of f(x) exceeds the graph of g(x).

• The graph of f(x) exceeds the graph of g(x) over the interval [0, 4], the graphs intersect at a point between 4 and 5, and then the graph of g(x) exceeds the graph of f(x).

• The first function has a higher y-intercept

• The second function has a higher y-intercept

• Both functions have the same y-intercept

• The y-intercepts are negative

• The slope of the first function is greater

• The slope of the second function is greater

• Both slopes are equal

• The slopes are equal in magnitude but opposite in sign