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5.05 Transformations of functions

Adaptive
Worksheet

Interactive practice questions

Consider the function $f\left(x\right)=9x-5$f(x)=9x5. Describe how the graph of the function $g\left(x\right)=f\left(x\right)+6$g(x)=f(x)+6 differs from the graph of $f\left(x\right)$f(x).

$f\left(x\right)$f(x) is vertically stretched by a factor of $6$6.

A

$f\left(x\right)$f(x) is translated up by $6$6 units.

B

$f\left(x\right)$f(x) is vertically compressed by a factor of $\frac{1}{6}$16.

C

$f\left(x\right)$f(x) is translated down by $6$6 units.

D
Hard
< 1min

Consider the function $f\left(x\right)=6x-9$f(x)=6x9. Describe how the graph of the function $g\left(x\right)=f\left(x\right)-2$g(x)=f(x)2 differs from $f\left(x\right)$f(x).

Hard
< 1min

Consider the function $f\left(x\right)=7x+7$f(x)=7x+7. Describe how the graph of the function $g\left(x\right)=6f\left(x\right)$g(x)=6f(x) differs from $f\left(x\right)$f(x).

Hard
< 1min

Consider the function $f\left(x\right)=3x+10$f(x)=3x+10. Describe how the graph of the function $g\left(x\right)=\frac{1}{6}f\left(x\right)$g(x)=16f(x) differs from $f\left(x\right)$f(x).

Hard
< 1min
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Outcomes

F.BF.A.1.B

Combine standard function types using arithmetic operations.

F.BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

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