Transformations of Exponential Functions

Front

What is a vertical translation in exponential functions?

Back

A vertical translation shifts the graph of the function up or down without changing its shape.

Front

What does a positive 'a' value indicate in an exponential function?

Back

It indicates that the graph will rise as x increases.

Front

What does a negative 'a' value indicate in an exponential function?

Back

It indicates that the graph will fall as x increases.

Front

What is a horizontal translation in exponential functions?

Back

A horizontal translation shifts the graph of the function left or right.

Front

What does the 'b' value represent in an exponential function y = a(b^x)?

Back

The 'b' value represents the base of the exponential function, which determines the rate of growth or decay.

Front

What is the effect of a vertical translation up by 3 on the function f(x) = 2^x?

Back

The new function will be f(x) = 2^x + 3, shifting the graph up by 3 units.

Front

What is the effect of a horizontal translation left by 2 on the function f(x) = 2^x?

Back

The new function will be f(x) = 2^(x + 2), shifting the graph left by 2 units.

Front

What is the range of the function f(x) = 2^x?

Back

The range is y > 0, meaning the output values are all positive.

Front

What is the transformation of the function f(x) = 2^(x - 1) + 2?

Back

It is a horizontal translation right by 1 and a vertical translation up by 2.

Front

What does the term 'asymptote' refer to in exponential functions?

Back

An asymptote is a line that the graph approaches but never touches, often the x-axis for exponential functions.