Explained: "Describe the transformations of f(x)=3{x} and h(x)=x3 that..."

iohanetc

Answered question

2020-11-01

Describe the transformations of

f (x) = \sqrt{3} {x}

and

h (x) = x^{3}

that result in the functions listed below.

g (x) = - \sqrt{3} {x - 3}

and

j (x) = - {(x - 3)}^{3}

p (x) = 4 \sqrt{3} {- x} - 1

and

q (x) = 0.25 {(- 4 x)}^{3} - 1

broliY

Skilled2020-11-02Added 97 answers

Step 1
We are given the functions:

f (x) = \sqrt{3} {x}

h (x) = x^{3}

Step 2
a) We write the transformations of the function

f (x)

to reach

g (x) = - \sqrt{3} {x - 3} :

\sqrt{3} {x} \to \sqrt{3} {x - 3}

(shift to the right with 3 units)

\sqrt{3} {x - 3} \to - \sqrt{3} {x - 3}

(reflection in the x-axis)
Step 3
We write the transformations of the function

h (x)

to reach

j (x) = - {(x - 3)}^{3}

x^{3} \to {(x - 3)}^{3}

(shift to the right with 3 units)

{(x - 3)}^{3} \to {(x - 3)}^{3}

(reflection in the x-axis)
Step 4
b). We write the transformations of the function

f (x)

to reach

p (x) = 4 \sqrt{3} {- x} - 1 :

\sqrt{3} {x} \to \sqrt{3} {- x}

(reflection in the y-axis)

\sqrt{3} {- x} \to 4 \sqrt{3} {- x}

(vertical strech)

4 \sqrt{3} {- x} \to 4 \sqrt{3} {- x} - 1

(shift down with 1 unit)
Step 5
We write the transformations of the function

h (x)

to reach

q (x) = 0.24 {(- 4 x)}^{3} - 1 :

x^{3} \to {(4 x)}^{3}

(horizontal shrink)

{(4 x)}^{3} \to {(- 4 x)}^{3}

(reflection in they-axis)

{(- 4 x)}^{3} \to 0.25 {(- 4 x)}^{3}

(vertical shrink)

0.25 {(- 4 x)}^{3} \to 0.25 {(- 4 x)}^{3} - 1

(shift down with 1 unit)

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