Exponential Functions From Tables & Graphs (Math Masters)

Which of the following is an example of an exponential function?

• f(x) = log(x)

• f(x) =2^x

• f(x) = x²

• f(x) = sin(x)

Answer explanation

An exponential function has the form f(x) = a^x, where a is a constant. The correct choice, f(x) = 2^x, fits this definition, while the others (logarithmic, polynomial, and trigonometric) do not.

What is the general form of an exponential function?

• f(x) = ax^b

• f(x) = a-b^x

• f(x) = ab^x

• f(x) = a+b^x

Answer explanation

The general form of an exponential function is f(x) = ab^x, where 'a' is a constant and 'b' is the base of the exponential. This distinguishes it from other forms like linear or polynomial functions.

Tags

CCSS.HSF.LE.A.2

If the value of y doubles as x increases by 1, what is the base b of the exponential function y=ab^x?

• 3

• 1

• 2

• 0.5

Answer explanation

If y doubles when x increases by 1, we have y = ab^x and 2y = ab^(x+1). Dividing gives 2 = b, so the base b of the exponential function is 2.

Tags

CCSS.HSF.LE.A.2

Given the table in the image shown, what type of function does this table represent?

• Linear

• Quadratic

• Exponential

• Constant

Answer explanation

The table represents an exponential function because the values increase at an increasing rate, indicating a multiplicative growth pattern rather than a constant or linear change.

Tags

CCSS.HSF-LE.A.1A

What is the y-intercept of the exponential function y=3⋅2^x?

• 2

• 3

• 0

• 6

Answer explanation

The y-intercept of an exponential function occurs when x=0. For y=3⋅2^x, substituting x=0 gives y=3⋅2^0=3⋅1=3. Thus, the y-intercept is 3.

Tags

CCSS.HSF-IF.C.7E

What is the rate of change for the exponential function shown?

• 4^x

• 3¹

• 2^x

• 5^x

Answer explanation

The rate of change for an exponential function is determined by its base. Here, 2^x indicates a growth rate of 2, making it the correct choice. Other options have different bases, thus not matching the required rate.

Tags

CCSS.HSF-IF.C.8B

If the function f(x)=4⋅3^x,what is f(2)?

• 24

• 36

• 12

• 48

Answer explanation

To find f(2), substitute x with 2 in the function: f(2) = 4 * 3^2 = 4 * 9 = 36. Therefore, the correct answer is 36.

Tags

CCSS.HSF-IF.C.8B

In an exponential growth function, as x approaches infinity, what happens to y?

• y approaches zero.

• y approaches infinity.

• y remains constant.

• y oscillates between values.

Answer explanation

In an exponential growth function, as x approaches infinity, y increases without bound, meaning y approaches infinity. This is characteristic of exponential growth, where values grow rapidly as x increases.

Tags

CCSS.HSF-IF.C.7E

Which of the following would be apart of an exponential decay function?

• A line with positive slope

• A line with negative slope

• A curve that rises steeply then levels off

• A curve that falls steeply

Answer explanation

An exponential decay function is characterized by a curve that falls steeply, indicating a rapid decrease in value over time. Therefore, the correct choice is 'A curve that falls steeply'.

Tags

CCSS.HSF-IF.C.7E

What is the base of the exponential function y=5⋅(0.5)^x?

• 1

• 2

• 5

• 0.5

Answer explanation

In the function y=5⋅(0.5)^x, the base of the exponential term is 0.5. This means that as x increases, the value of y decreases, indicating a decay function. Thus, the correct answer is 0.5.

Tags

CCSS.HSF-IF.C.8B