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 a vertical stretch by a factor of k do to the function f(x)?

Back

It multiplies the output of the function by k, making the graph taller.

Front

What does a horizontal shrink by a factor of k do to the function f(x)?

Back

It compresses the graph horizontally, making it narrower by a factor of k.

Front

What is the effect of adding a constant to a function, such as f(x) + c?

Back

It shifts the graph vertically by c units; if c is positive, it shifts up, and if negative, it shifts down.

Front

What is the effect of subtracting a constant from the input of a function, such as f(x - c)?

Back

It shifts the graph horizontally to the right by c units.

Front

What does the transformation f(-x) represent?

Back

It reflects the graph of f(x) across the y-axis.

Front

What does the transformation -f(x) represent?

Back

It reflects the graph of f(x) across the x-axis.

Front

What is the effect of multiplying the function by a negative number, such as -f(x)?

Back

It reflects the graph across the x-axis.

Front

What does the transformation f(kx) do, where k > 1?

Back

It compresses the graph horizontally by a factor of 1/k.

Front

What does the transformation f(kx) do, where 0 < k < 1?

Back

It stretches the graph horizontally by a factor of 1/k.