HW: Exponential Functions and Asymptotes

Front

What does the 'a' represent in an exponential function?

Back

Y-intercept/Initial value

Front

Is the function y = 0.5(2)^x an example of exponential growth or decay?

Back

Exponential growth

Front

What is an asymptote in the context of exponential functions?

Back

A horizontal line which the values of the function cannot fall below.

Front

What is the y-intercept of the function y = 2^x + 5?

Back

5

Front

Identify the equation that represents exponential decay: y = 3(0.5)^x or y = 2(2)^x.

Back

y = 3(0.5)^x

Front

What is the general form of an exponential function?

Back

y = a(b)^x, where 'a' is the initial value and 'b' is the growth/decay factor.

Front

What does a growth factor greater than 1 indicate in an exponential function?

Back

The function is experiencing exponential growth.

Front

What does a growth factor between 0 and 1 indicate in an exponential function?

Back

The function is experiencing exponential decay.

Front

How do you find the horizontal asymptote of an exponential function?

Back

The horizontal asymptote is typically y = 0 for functions of the form y = a(b)^x.

Front

What is the effect of changing the value of 'a' in the function y = a(b)^x?

Back

Changing 'a' affects the vertical stretch or compression and the initial value of the function.