Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the position, size, or shape of its graph.

Front

What does f(x + c) represent?

Back

A horizontal shift of the graph of f(x) to the left by c units if c is positive, and to the right if c is negative.

Front

What does f(x) + k represent?

Back

A vertical shift of the graph of f(x) upward by k units if k is positive, and downward if k is negative.

Front

What does -f(x) represent?

Back

A reflection of the graph of f(x) over the x-axis.

Front

What does f(-x) represent?

Back

A reflection of the graph of f(x) over the y-axis.

Front

What is the effect of multiplying a function by a factor less than 1?

Back

It results in a vertical shrink of the graph.

Front

What is the effect of multiplying a function by a factor greater than 1?

Back

It results in a vertical stretch of the graph.

Front

What does f(kx) represent where k > 1?

Back

A horizontal shrink of the graph of f(x) by a factor of k.

Front

What does f(kx) represent where 0 < k < 1?

Back

A horizontal stretch of the graph of f(x) by a factor of 1/k.

Front

How do you shift the graph of f(x) = x^2 down by 4 units?

Back

The new function is f(x) = x^2 - 4.