Transformations of Linear Functions

Front

What is a vertical translation of a graph?

Back

A vertical translation of a graph occurs when the entire graph is shifted up or down along the y-axis. For example, if the function f(x) is translated vertically by 2 units up, the new function is g(x) = f(x) + 2.

Front

What does it mean when a graph is reflected over the x-axis?

Back

When a graph is reflected over the x-axis, all y-values of the function are multiplied by -1. For example, if f(x) is the original function, the reflected function is g(x) = -f(x).

Front

How does the equation y = f(x) + c affect the graph of f(x)?

Back

The equation y = f(x) + c shifts the graph of f(x) vertically. If c is positive, the graph shifts up by c units; if c is negative, it shifts down by |c| units.

Front

What is a vertical stretch of a graph?

Back

A vertical stretch occurs when the y-values of a function are multiplied by a factor greater than 1. For example, if f(x) is stretched by a factor of 2, the new function is g(x) = 2f(x).

Front

What is a vertical compression of a graph?

Back

A vertical compression occurs when the y-values of a function are multiplied by a factor between 0 and 1. For example, if f(x) is compressed by a factor of 1/2, the new function is g(x) = (1/2)f(x).

Front

What does the equation g(x) = f(x) + 4 represent?

Back

The equation g(x) = f(x) + 4 represents a vertical translation of the graph of f(x) upward by 4 units.

Front

What is the effect of the equation g(x) = 3f(x)?

Back

The equation g(x) = 3f(x) represents a vertical stretch of the graph of f(x) by a factor of 3.

Front

How does the equation g(x) = (1/3)f(x) transform the graph of f(x)?

Back

The equation g(x) = (1/3)f(x) represents a vertical compression of the graph of f(x) by a factor of 1/3.

Front

What transformation occurs when the function f(x) is replaced with -f(x)?

Back

Replacing f(x) with -f(x) reflects the graph of f(x) over the x-axis.

Front

What does the equation g(x) = f(x - 2) represent?

Back

The equation g(x) = f(x - 2) represents a horizontal translation of the graph of f(x) to the right by 2 units.