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 shift of a function mean?

Back

A vertical shift moves the graph of the function up or down. For example, if f(x) is shifted up by 3, the new function is f(x) + 3.

Front

What does a horizontal shift of a function mean?

Back

A horizontal shift moves the graph of the function left or right. For example, if f(x) is shifted left by 2, the new function is f(x + 2).

Front

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

Back

The negative sign reflects the graph of the function across the x-axis.

Front

What does the transformation f(x - c) represent?

Back

The transformation f(x - c) represents a horizontal shift to the right by c units.

Front

What does the transformation f(x + c) represent?

Back

The transformation f(x + c) represents a horizontal shift to the left by c units.

Front

What is the effect of multiplying a function by a factor greater than 1, such as 2f(x)?

Back

Multiplying a function by a factor greater than 1 vertically stretches the graph away from the x-axis.

Front

What is the effect of multiplying a function by a factor between 0 and 1, such as 0.5f(x)?

Back

Multiplying a function by a factor between 0 and 1 vertically compresses the graph towards the x-axis.

Front

What does the transformation g(x) = f(x) + k represent?

Back

The transformation g(x) = f(x) + k represents a vertical shift of the graph of f(x) upward by k units if k > 0, and downward if k < 0.

Front

What is the equation of the transformation that shifts the graph of f(x) = x^2 to the left by 3 units?

Back

The equation is g(x) = f(x + 3) = (x + 3)^2.