Function Notation Transformations Check Point

Front

What is function notation?

Back

Function notation is a way to represent functions in mathematics, typically using symbols like f(x) to denote the output of a function f for a given input x.

Front

What does a vertical compression by a factor of k mean?

Back

A vertical compression by a factor of k (where 0 < k < 1) means that the output values of the function are multiplied by k, making the graph 'squish' towards the x-axis.

Front

What does a vertical stretch by a factor of k mean?

Back

A vertical stretch by a factor of k (where k > 1) means that the output values of the function are multiplied by k, making the graph 'stretch' away from the x-axis.

Front

What is the effect of replacing f(x) with f(x + c)?

Back

Replacing f(x) with f(x + c) shifts the graph of the function horizontally to the left by c units if c is positive, and to the right if c is negative.

Front

What is the effect of replacing f(x) with f(x - c)?

Back

Replacing f(x) with f(x - c) shifts the graph of the function horizontally to the right by c units if c is positive, and to the left if c is negative.

Front

What does the transformation g(x) = f(x) + k do to the graph?

Back

The transformation g(x) = f(x) + k shifts the graph of f(x) vertically upward by k units if k is positive, and downward if k is negative.

Front

What is the effect of a negative sign in front of a function, such as -f(x)?

Back

A negative sign in front of a function reflects the graph across the x-axis.

Front

How does the transformation g(x) = f(-x) affect the graph?

Back

The transformation g(x) = f(-x) reflects the graph of f(x) across the y-axis.

Front

What does the transformation g(x) = af(x) do when a > 1?

Back

When a > 1, the transformation g(x) = af(x) results in a vertical stretch of the graph by a factor of a.

Front

What does the transformation g(x) = af(x) do when 0 < a < 1?

Back

When 0 < a < 1, the transformation g(x) = af(x) results in a vertical compression of the graph by a factor of a.