Exceeding 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 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).

Which statement BEST describes the comparison of the function values for f(x) and g(x)?

• The values of f(x) will always exceed the values of g(x).

• The values of g(x) will always exceed the values of f(x).

• The values of f(x) exceed the values of g(x) over the interval [0, 5].

• The values of g(x) begin to exceed the values of f(x) within the interval [4, 5].

The image shows the graphs of a linear function, f(x), exponential function, g(x), and quadratic function, h(x).

Over what positive interval does f(x) exceed g(x)?

• (0,6)

• (0,5.5)

• (6,∞)

• (-∞,6)

True or False: All increasing exponential functions eventually exceed all increasing linear functions.

• True

• False

For what positive minimum value of x will f(x) exceed g(x)?

• x = 3

• x = 5

• x = 7

• x = 8

• The exponential function NEVER exceeds the linear Functions

• The exponential functions ALWAYS exceeds the linear function

• The linear function exceeds the exponential function over the interval [0, 4]

• The exponential function exceeds the Linear functions over the interval [3, 4]

• The exponential function exceeds the Linear functions over the interval [4, 5]

Which statement below describes the comparison of rate of change between the linear function f(x) and the exponential function g(x).

• g(x) rate of change is ALWAYS greater than f(x) rate of change.

• g(x) is NEVER greater than f(x) rate of change.

• g(x) will eventually exceed the rate of change of f(x).

• There is not enough information to compare the rate of change of f(x) to g(x).

The image shows the graphs of a linear function, f(x), exponential function, g(x), and quadratic function, h(x).

Using only what can be seen in the image, for what positive values does g(x) exceed h(x)?

• (0,1)

• (1,0)

• (1,∞)

• (1,6)