Exponential Functions vs Linear Graphs

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

• True

• False

• 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).

Which statement below is TRUE regarding the two functions?

• Both functions are linear

• Both functions are increasing

• Both functions have a y-intercept of 1

• Both functions are exponential growth

Two functions are shown below. f(x) = 1/2 * 2^x g(x) = 5x + 2 What is the largest integer value of x such that f(x) ≤ g(x)?

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For the functions f(x) = 1/2 * 2^x and g(x) = 5x + 2, what is the largest integer value of x such that f(x) <= g(x)?

• 3

• 4

• 5

• 6

Which function describes the graph?

• Linear

• Exponential

• neither

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)

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)

• Exponential Functions NEVER exceed Linear Functions

• Exponential Functions ALWAYS exceed Linear Functions

• The linear function exceeds the exponential function over the interval [0, 6]

• The exponential function exceeds the Linear functions over the interval [5, 6]