2.6 Families of Functions Classwork

Front

What is a horizontal translation of a function?

Back

A horizontal translation shifts the graph of a function left or right without changing its shape.

Front

How does the function y = (x + 3)^2 relate to the parent function y = x^2?

Back

It represents a horizontal translation of the parent function 3 units to the left.

Front

What does the transformation g(x) = f(x) + 6 indicate?

Back

It indicates a vertical translation of the function f(x) 6 units up.

Front

Write the equation for a vertical translation of y = f(x) 2 units up.

Back

f(x) = f(x) + 2.

Front

What is a reflection of a function over the x-axis?

Back

A reflection over the x-axis flips the graph of the function vertically.

Front

How do you reflect the function f(x) = x + 1 over the x-axis?

Back

The reflected function is f(x) = -x - 1.

Front

What is a vertical stretch of a function?

Back

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

Front

Write the equation for a vertical stretch of y = x by a factor of 2.

Back

y = 2x.

Front

What is the effect of adding a constant to a function?

Back

Adding a constant shifts the graph vertically; positive values shift up, negative values shift down.

Front

What does the transformation y = (x - 4)^2 represent?

Back

It represents a horizontal translation of the parent function 4 units to the right.