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 type of pattern do exponential functions have?

Back

Exponential functions multiply or divide by the same number every time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a(b^x) where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a(b^x) where 0 < b < 1.

Front

How do you identify exponential growth from a table of values?

Back

In exponential growth, as x increases, the y values increase rapidly.

Tags

CCSS.HSF-LE.A.1A

Front

How do you identify exponential decay from a table of values?

Back

In exponential decay, as x increases, the y values decrease rapidly.

Front

What is the value of f(0) in an exponential function f(x) = a(b^x)?

Back

f(0) = a, since b^0 = 1.

Tags

CCSS.HSF-IF.C.8B

Front

What does the base 'b' represent in an exponential function?

Back

The base 'b' represents the growth (b > 1) or decay (0 < b < 1) factor.

Tags

CCSS.HSF-IF.C.8B

Front

What is the effect of changing the value of 'a' in the function f(x) = a(b^x)?

Back

Changing 'a' affects the vertical stretch or compression of the graph.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept is the point where the graph crosses the y-axis, which occurs at (0, a).

Tags

CCSS.HSF-IF.C.7E