Transformations of Linear Functions

Front

What is a vertical compression of a function?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph 'squish' towards the x-axis.

Front

What happens to the graph of a function when it is reflected across the x-axis?

Back

When a function is reflected across the x-axis, all the y-values of the function are multiplied by -1, resulting in an upside-down version of the original graph.

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph 'stretch' away from the x-axis.

Front

How does the equation y = f(x) + k transform the graph of f(x)?

Back

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

Front

What does the transformation y = -f(x) represent?

Back

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

Front

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

Back

Replacing f(x) with f(x - h) translates the graph of f(x) horizontally to the right by h units.

Front

What does the transformation y = f(x + h) do to the graph of f(x)?

Back

The transformation y = f(x + h) translates the graph of f(x) horizontally to the left by h units.

Front

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

Back

The equation y = af(x) vertically stretches or compresses the graph of f(x) depending on the value of a. If |a| > 1, it stretches; if 0 < |a| < 1, it compresses.

Front

What is the parent function of linear functions?

Back

The parent function of linear functions is f(x) = x, which represents a straight line with a slope of 1 and a y-intercept of 0.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the graph.