Unit 6 Exponential and Logarithmic Graphs

Front

What is an asymptote?

Back

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

Front

Given the function y=3^x, what is the horizontal asymptote?

Back

y=0

Front

What characterizes exponential growth?

Back

Exponential growth occurs when a quantity increases by a constant percentage over time, represented by functions of the form y=a(b^x) where b>1.

Front

What characterizes exponential decay?

Back

Exponential decay occurs when a quantity decreases by a constant percentage over time, represented by functions of the form y=a(b^x) where 0

Front

What is the range of the function y=6?

Back

The range is {6} since it is a constant function.

Front

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

Back

The range is (0, ∞) because the output of the function is always positive.

Front

What is the general form of an exponential function?

Back

The general form is y=a(b^x), where a is a constant, b is the base, and x is the exponent.

Front

What does the base of an exponential function indicate?

Back

The base indicates the growth or decay factor. If b>1, the function represents growth; if 0

Front

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

Back

The y-intercept is 5, which occurs when x=0.

Front

How do you determine if a function is exponential?

Back

A function is exponential if it can be expressed in the form y=a(b^x) where a is a non-zero constant and b is a positive constant.