Comparing Functions

How much greater is the x-intercept of f(x) = (x - 7)² than the x-intercept of g(x)=√(x-1)

Mathematical Equivalence

ON

Which grows bigger? f(x) = 2x + 3 or g(x) = 0.5x² - 3?

• f(x)

• g(x)

• They grow at the same rate

• A

• B

• C

Which statement is true about the graphs of exponential growth functions?

• The graphs of exponential functions never exceed the graphs of linear and quadratic functions

• The graphs of exponential functions always exceed the graphs of linear and quadratic functions

• The graphs of exponential functions eventually exceed the graphs of linear and quadratic functions

• The graphs of exponential functions always exceed the graphs of linear functions but not quadratic functions

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 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 between 4 and 5, and then the graph of g(x) exceeds the graph of f(x)

What is the sum of the the x-intercepts for y = (x + 5)² and y = √(x+2)?

Mathematical Equivalence

ON

• A

• B

• C

• D

Reorder the following, placing the one that increases the most, first.

• r(x)

• h(x)

• f(x)

• g(x)

Which has the smallest y-intercept?

• A

• B

• C

• D

Graph: y = x² -8x +18