CHAPTER 10
SECTION 10.5
Transformations with Functions
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 \(g(x)=kf(x)\)?
Answer Key
Transformations with Functions
- 1.B. \(h(x)=|x-2|\)
- 2.D. \(k(x)=(x+3)^2\)
- 3.C. \(h(x)=(x-4)^2-3\)
- 4.D. Don said that the graph of \(g(x)\) is narrower and shifted right 3 units.
- 5.D. 4