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1.03 Function transformations

Adaptive
Worksheet

Interactive practice questions

Consider the graphs of $f\left(x\right)=\frac{3}{x}$f(x)=3x and $g\left(x\right)$g(x).

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A coordinate plane is shown with two parabolas plotted on it: f(x), drawn in gray line and g(x) drawn in black line. Asymptote of the parabolas are indicated by dotted line. Both function of parabolas have a vertical asymptote of at $x=0$x=0. f(x) has its horizontal asymptote on $y=0$y=0. g(x) has its horizontal asymptote on $y=-3$y=3. The asymptotes are not explicitly labeled on the graph.
a

Which of the following transformations can be used to describe $g\left(x\right)$g(x)?

$g\left(x\right)=f\left(x-3\right)$g(x)=f(x3)

A

$g\left(x\right)=f\left(-x\right)$g(x)=f(x)

B

$g\left(x\right)=-f\left(x\right)$g(x)=f(x)

C

$g\left(x\right)=f\left(x\right)$g(x)=f(x) $-$ $3$3

D

$g\left(x\right)=-3f\left(x\right)$g(x)=3f(x)

E
b

State the equation of $g\left(x\right)$g(x).

Easy
1min

Consider the following graph.

Easy
1min

Consider the following graph.

Easy
1min

Consider the graphs of $f\left(x\right)=\frac{2}{x}$f(x)=2x and $g\left(x\right)$g(x).

Easy
1min
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Outcomes

A2.F.1

The student will investigate, analyze, and compare square root, cube root, rational, exponential, and logarithmic function families, algebraically and graphically, using transformations.

A2.F.1b

Write the equation of a square root, cube root, rational, exponential, and logarithmic function, given a graph, using transformations of the parent function, including f(x) + k; f(kx); f(x + k); and kf(x), where k is limited to rational values. Transformations of exponential and logarithmic functions, given a graph, should be limited to a single transformation.

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