Transformations of functions

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 taller.

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 shorter.

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means that for every point (x, y) on the graph, the point (x, -y) is also on the graph.

Front

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

Back

This transformation shifts the graph of the function f(x) vertically by k units. If k is positive, it shifts up; if k is negative, it shifts down.

Front

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

Back

This transformation shifts the graph of the function f(x) horizontally by h units. If h is positive, it shifts left; if h is negative, it shifts right.

Front

What is the effect of multiplying a function by a negative number?

Back

Multiplying a function by a negative number reflects the graph over the x-axis.

Front

What is the effect of multiplying a function by a factor of 2?

Back

Multiplying a function by a factor of 2 vertically stretches the graph by a factor of 2.

Front

What is the effect of multiplying a function by a factor of 1/2?

Back

Multiplying a function by a factor of 1/2 vertically compresses the graph by a factor of 2.

Front

What type of transformation is represented by y = -f(x)?

Back

This transformation reflects the graph of the function f(x) over the x-axis.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.