Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the graph of the function in some way, such as shifting, reflecting, stretching, or compressing.

Front

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

Back

Reflecting a function over the x-axis means to take each point (x, y) on the graph and map it to (x, -y). This changes the sign of the output values.

Front

What is the effect of the transformation y = f(x) + k?

Back

The transformation y = f(x) + k shifts 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 is the effect of the transformation y = f(x - h)?

Back

The transformation y = f(x - h) shifts the graph of f(x) horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

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

Back

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

Front

How does the transformation y = f(-x) affect the graph of f(x)?

Back

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

Front

What is the effect of the transformation y = af(x) where a > 1?

Back

The transformation y = af(x) vertically stretches the graph of f(x) by a factor of a.

Front

What is the effect of the transformation y = af(x) where 0 < a < 1?

Back

The transformation y = af(x) vertically compresses the graph of f(x) by a factor of a.

Front

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

Back

The transformation y = f(kx) horizontally compresses the graph of f(x) by a factor of 1/k if k > 1, or stretches it by a factor of 1/k if 0 < k < 1.

Front

What is the equation of a quadratic function reflected over the x-axis?

Back

The equation of a quadratic function reflected over the x-axis is y = -x^2 + k, where k is a constant.