transformation of functions

Front

What is a transformation of a function?

Back

A transformation of a function refers to the changes made to the graph of the function, which can include shifts, stretches, compressions, and reflections.

Front

What does shifting a function to the right mean?

Back

Shifting a function to the right means adding a positive value to the input variable (x) in the function's equation.

Front

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

Back

This transformation shifts the graph of the function vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

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

Back

This transformation shifts the graph of the function horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output of the function is 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 of the function is multiplied by a factor between 0 and 1, making the graph shorter.

Front

What does the transformation f(x) = af(x) do, where a > 1?

Back

This transformation vertically stretches the graph of the function by a factor of a.

Front

What does the transformation f(x) = af(x) do, where 0 < a < 1?

Back

This transformation vertically compresses the graph of the function by a factor of a.

Front

What is the effect of the transformation f(x) = -f(x)?

Back

This transformation reflects the graph of the function across the x-axis.

Front

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

Back

This transformation reflects the graph of the function across the y-axis.