MINI LESSON

Transformations with Functions

Transformations change the position or shape of a graph.

Adding or subtracting outside the function shifts the graph up or down.

Adding or subtracting inside the function shifts the graph left or right.

Multiplying a function can stretch, compress, or reflect its graph.

Question 1

Which function represents the graph of \(w(x)=|x|\) shifted 2 units to the right?

Question 2

Given \(f(x)=x^2\), which function will shift \(f(x)\) to the left 3 units?

Question 3

If \(f(x)=x^2\), then which function represents a shift of the graph of \(f(x)\) 4 units to the right and 3 units down?

Question 4

The students in Mrs. Smith's algebra class were asked to describe the graph of \(g(x)=2(x-3)^2\) compared to the graph of \(f(x)=x^2\). Which student response is correct?

Question 5

The function \(f(x)=x^2\) is multiplied by \(k\), where \(k<-1\). Which graph could represent \(g(x)=kf(x)\)?