Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the value of f(0), which equals 'a'.

Tags

CCSS.HSF-IF.C.7E

Front

How do you identify the initial value in an exponential function?

Back

The initial value in an exponential function f(x) = a * b^x is represented by 'a', which is the value of the function when x = 0.

Tags

CCSS.HSF.LE.B.5

Front

What does the base of an exponential function indicate?

Back

The base of an exponential function indicates the growth (if b > 1) or decay (if 0 < b < 1) rate of the function.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a * b^x, where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a * b^x, where 0 < b < 1.

Tags

CCSS.HSF-LE.A.1A

Front

How do you find the y-intercept of the function f(x) = 5(3)^x?

Back

The y-intercept is found by evaluating f(0): f(0) = 5(3)^0 = 5.

Tags

CCSS.HSF-IF.C.7E

Front

What is the y-intercept of the function f(x) = 2(0.5)^x?

Back

The y-intercept is f(0) = 2(0.5)^0 = 2.

Tags

CCSS.HSF-IF.C.7E

Front

If f(x) = 4(2)^x, what is the initial value?

Back

The initial value is 4.

Tags

CCSS.HSF.LE.B.5

Front

What is the effect of changing the base in an exponential function?

Back

Changing the base affects the rate of growth or decay; a larger base results in faster growth, while a smaller base (greater than 0) results in slower growth or faster decay.

Tags

CCSS.HSF-IF.C.7E