Transformations of Exponential Functions

Front

What transformation occurs from y=2^x to y=-1⋅2^x?

Back

Reflection over the x-axis

Front

What is the transformation from the parent graph f(x)=2^x to g(x)=2^(x-3)?

Back

Horizontally shift right 3

Front

What is the parent function of f(x)=2(1/2)^x-7?

Back

f(x)=(1/2)^x

Front

How does the graph of y=4^x change to y=2(4)^(x-3)+1?

Back

Vertically stretched by a factor of 2, right 3, and up 1

Front

What does a negative coefficient in front of an exponential function indicate?

Back

Reflection over the x-axis.

Front

What effect does a positive coefficient greater than 1 have on an exponential function?

Back

It vertically stretches the graph.

Front

What does a horizontal shift to the right by k units do to the function f(x)?

Back

It transforms f(x) to f(x-k).

Front

What is the effect of a vertical shift of c units on the function f(x)?

Back

It transforms f(x) to f(x) + c.

Front

How do you identify the parent function of an exponential function?

Back

The parent function is the simplest form of the exponential function, typically f(x)=b^x where b>0.

Front

What is the transformation from f(x)=b^x to f(x)=b^(x-h)?

Back

A horizontal shift to the right by h units.