Function Transformations

Front

What is a function transformation?

Back

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

Front

What does the transformation p(x) = f(x + 3) represent?

Back

The graph of f(x) is shifted left by 3 units.

Front

What does the transformation h(x) = f(x) + 2 represent?

Back

The graph of f(x) is shifted up by 2 units.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is y = x².

Front

What type of function is represented by the equation y = |x|?

Back

The function is an absolute value function.

Front

What type of function is represented by the equation y = √x?

Back

The function is a square root function.

Front

What does a vertical stretch of a function do?

Back

A vertical stretch increases the distance between points on the graph and the x-axis.

Front

What does a horizontal shift to the right mean in function transformations?

Back

A horizontal shift to the right means the graph of the function moves away from the y-axis.

Front

What is the effect of a negative sign in front of a function, such as -f(x)?

Back

The graph of the function is reflected over the x-axis.

Front

What does the transformation f(x) = 2f(x) represent?

Back

This transformation represents a vertical stretch by a factor of 2.