PH: L3.1 Exponential Functions and Their Graphs

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 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 of the function.

Tags

CCSS.HSF-IF.C.8B

Front

What does it mean for an exponential function to grow?

Back

An exponential function grows when the base 'b' is greater than 1, resulting in values that increase rapidly as 'x' increases.

Tags

CCSS.HSF-IF.C.8B

Front

What does it mean for an exponential function to decay?

Back

An exponential function decays when the base 'b' is between 0 and 1, resulting in values that decrease rapidly as 'x' increases.

Tags

CCSS.HSF-IF.C.8B

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 graph an exponential function?

Back

To graph an exponential function, plot the y-intercept, identify the growth or decay direction based on the base, and draw a smooth curve that approaches the x-axis but never touches it.

Tags

CCSS.HSF-IF.C.7E

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 reaches as x approaches negative infinity.

Tags

CCSS.HSF-IF.C.7E

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, represented as (-∞, ∞).

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What is the range of an exponential function?

Back

The range of an exponential function is all positive real numbers, represented as (0, ∞).

Front

How does changing the base of an exponential function affect its graph?

Back

Changing the base of an exponential function affects the steepness of the graph; a larger base results in a steeper curve.

Tags

CCSS.HSF-IF.C.7E