AP Precalculus Exponential Functions Review

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.

Tags

TEKS.MATH.A.12B

TEKS.MATH.A.9B

Front

What is the base of an exponential function?

Back

The base of an exponential function is the constant 'b' in the function f(x) = a * b^x. It determines the rate of growth or decay.

Tags

TEKS.MATH.P.9B

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.

Tags

TEKS.MATH.A.12B

TEKS.MATH.A.9B

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.

Front

How do you identify exponential growth from a graph?

Back

Exponential growth is identified by a curve that rises steeply as x increases, indicating that the function's value increases rapidly.

Tags

TEKS.MATH.2A.2A

TEKS.MATH.2A.5A

TEKS.MATH.A.9D

TEKS.MATH.P.2F

TEKS.MATH.P.2G

Front

How do you identify exponential decay from a graph?

Back

Exponential decay is identified by a curve that falls steeply as x increases, indicating that the function's value decreases rapidly.

Tags

TEKS.MATH.2A.2A

TEKS.MATH.2A.5A

TEKS.MATH.A.9D

TEKS.MATH.P.2F

TEKS.MATH.P.2K

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

TEKS.MATH.2A.2A

TEKS.MATH.2A.5A

TEKS.MATH.A.9D

TEKS.MATH.P.2F

TEKS.MATH.P.2G

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is the line y = 0, which the graph approaches but never touches as x approaches negative infinity.

Tags

TEKS.MATH.2A.2A

TEKS.MATH.2A.5A

TEKS.MATH.A.9D

TEKS.MATH.P.2F

TEKS.MATH.P.2K

Front

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

Back

Changing the base 'b' affects the rate of growth or decay; a larger base results in faster growth, while a smaller base (greater than 1) results in slower growth.

Tags

TEKS.MATH.2A.5A

TEKS.MATH.A.9D

TEKS.MATH.P.2F

TEKS.MATH.P.2G

TEKS.MATH.P.2K

Front

What is the inverse of an exponential function?

Back

The inverse of an exponential function is a logarithmic function, expressed as f^-1(x) = log_b(x/a).

Tags

TEKS.MATH.P.2E