Exponential Function Flashcard

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 a positive real number, and 'x' is the exponent.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is a horizontal line that the graph approaches as x approaches positive or negative infinity. For functions of the form f(x) = a * b^x, the horizontal asymptote is typically y = 0.

Tags

CCSS.HSF-IF.C.7E

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'. It represents the initial value of the function.

Tags

CCSS.HSF-IF.C.7E

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' in f(x) = a * b^x is greater than 1, leading to an increase in value as x increases. Exponential decay occurs when 'b' is between 0 and 1, resulting in a decrease in value as x increases.

Tags

CCSS.HSF-IF.C.8B

Front

How do you identify exponential growth from a graph?

Back

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

Tags

CCSS.HSF-IF.C.7E

Front

How do you identify exponential decay from a graph?

Back

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

Tags

CCSS.HSF-IF.C.7E

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(x) = a * b^x, where 'a' is the initial value and 'b' > 1.

Tags

CCSS.HSF-LE.A.1A

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(x) = a * b^x, where 'a' is the initial value and 0 < b < 1.

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

In an exponential function f(x) = a * b^x, the base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

Tags

CCSS.HSF-IF.C.8B

Front

What is the significance of the initial value 'a' in an exponential function?

Back

The initial value 'a' in an exponential function f(x) = a * b^x represents the value of the function when x = 0, indicating the starting point of the function.

Tags

CCSS.HSF.LE.B.5