Graphing Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = 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 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 y = a * b^x, the horizontal asymptote is typically y = 0.

Front

What does the base of an exponential function determine?

Back

The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

What is the domain of the function y = 2^x?

Back

The domain of the function y = 2^x is all real numbers, expressed as (-∞, ∞).

Front

What is the range of the function y = 2^x?

Back

The range of the function y = 2^x is all positive real numbers, expressed as (0, ∞).

Front

How does a vertical shift affect the graph of an exponential function?

Back

A vertical shift moves the graph up or down. For example, y = 2^x + 3 shifts the graph of y = 2^x up by 3 units.

Front

How does a horizontal shift affect the graph of an exponential function?

Back

A horizontal shift moves the graph left or right. For example, y = 2^(x - 1) shifts the graph of y = 2^x to the right by 1 unit.

Front

What is the effect of a negative exponent in an exponential function?

Back

A negative exponent indicates a reciprocal. For example, y = 2^(-x) is equivalent to y = 1/(2^x), which represents exponential decay.

Front

What is the parent function of exponential functions?

Back

The parent function of exponential functions is y = b^x, where b is a positive constant. Common examples include y = 2^x and y = 3^x.

Front

What is the significance of the y-intercept in an exponential function?

Back

The y-intercept of an exponential function occurs at x = 0. For y = a * b^x, the y-intercept is (0, a), indicating the initial value of the function.