Transformations 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 a function, which can include shifts, stretches, compressions, and reflections.

Front

What does a horizontal shift to the right by 2 units mean?

Back

It means that every point on the graph of the function moves 2 units to the right along the x-axis.

Front

What does a vertical stretch by a factor of 3 do to a function?

Back

It multiplies the y-values of the function by 3, making the graph taller.

Front

What is the effect of a vertical compression by a factor of 1/3?

Back

It reduces the y-values of the function to one-third of their original values, making the graph shorter.

Front

How does the equation f(x) = ⅔(x - 7)² transform the parent function y = x²?

Back

It shrinks the graph vertically by a factor of ⅔ and shifts it to the right by 7 units.

Front

What does the notation f(x - 2) indicate?

Back

It indicates a horizontal shift of the function f(x) to the right by 2 units.

Front

What is the transformation represented by the equation y = -2|x - 3| + 3?

Back

It reflects the graph over the x-axis, stretches it vertically by a factor of 2, shifts it right by 3 units, and shifts it up by 3 units.

Front

What does a reflection over the x-axis do to a function?

Back

It flips the graph of the function over the x-axis, changing the sign of all y-values.

Front

What is the parent function of y = |x|?

Back

The parent function of y = |x| is the absolute value function, which outputs the non-negative value of x.

Front

How do you identify a vertical stretch in a function?

Back

A vertical stretch occurs when the coefficient of the function is greater than 1, which increases the distance of points from the x-axis.