Question

Vertical Stretches and Vertical Compressions

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(1 point)
Part A: Complete the table to vertically stretch the parent functionf(x)=x3
by a factor of 3. Write your answer as a whole number of decimal

x y=kf(x)=_x3
0 -
1 _
2 _
Part B: Complete the table to show that y=kf(x)
results in the parent function being vertically compressed when k=12
. Write your answer as a whole number of decimal

x y=kf(x)=_x4
0 _
1 _
2 _

Answer 1

To complete the tables for the transformations of the given parent functions, we'll apply the specified factors:

### Part A: Vertically Stretching \( f(x) = x^3 \) by a Factor of 3

The transformation for a vertical stretch by a factor \( k \) can be expressed as:

\[
y = k f(x) = 3 f(x) = 3 x^3
\]

Now we will plug in the values of \( x \) into the equation to find \( y \).

#### Table Calculation
- For \( x = 0 \):
\[
y = 3 (0^3) = 3 \times 0 = 0
\]

- For \( x = 1 \):
\[
y = 3 (1^3) = 3 \times 1 = 3
\]

- For \( x = 2 \):
\[
y = 3 (2^3) = 3 \times 8 = 24
\]

### Completed Table for Part A:
| x | y = kf(x) = 3x³ |
|---|------------------|
| 0 | 0 |
| 1 | 3 |
| 2 | 24 |

---

### Part B: Vertically Compressing \( f(x) = x^4 \) by a Factor of \( \frac{1}{2} \)

The transformation for a vertical compression by a factor \( k \) can be expressed as:

\[
y = k f(x) = \frac{1}{2} f(x) = \frac{1}{2} x^4
\]

Now we will plug in the values of \( x \) into the equation to find \( y \).

#### Table Calculation
- For \( x = 0 \):
\[
y = \frac{1}{2} (0^4) = \frac{1}{2} \times 0 = 0
\]

- For \( x = 1 \):
\[
y = \frac{1}{2} (1^4) = \frac{1}{2} \times 1 = 0.5
\]

- For \( x = 2 \):
\[
y = \frac{1}{2} (2^4) = \frac{1}{2} \times 16 = 8
\]

### Completed Table for Part B:
| x | y = kf(x) = \( \frac{1}{2} x^4 \) |
|---|----------------------------------|
| 0 | 0 |
| 1 | 0.5 |
| 2 | 8 |

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