BR 11/4/24 Exponential Functions - Graphs & Tables

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 of the exponential (a positive real number), and 'x' is the exponent.

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 general form of an exponential function?

Back

The general form of an exponential function is y = a(b^x), where 'a' is a constant that affects the vertical stretch or compression, and 'b' is the base.

Front

How do you find the y-intercept of an exponential function?

Back

To find the y-intercept of an exponential function, substitute x = 0 into the function and solve for y.

Front

What is the y-intercept of the function y = 3(2^x)?

Back

The y-intercept is (0, 3), since when x = 0, y = 3(2^0) = 3.

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is typically the line y = 0.

Front

What is the horizontal asymptote of the function y = 2^x?

Back

The horizontal asymptote of the function y = 2^x is y = 0.

Front

Does the function y = 3(2^x) have an x-intercept?

Back

No, the function y = 3(2^x) does not have an x-intercept because exponential functions do not cross the x-axis.

Front

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

Back

The y-intercept indicates the initial value of the function when x = 0, which is important for understanding the function's behavior.

Front

How can you determine if an exponential function is increasing or decreasing?

Back

An exponential function is increasing if the base 'b' is greater than 1 and decreasing if the base 'b' is between 0 and 1.