Question

Complete the table to vertically stretch the parent function f(x) = x^2 by a factor of 3 write your answer as a whole number of decimal
x y=kf(x)=___x^3
0 ____
1 ___
2 ___
Complete the table to show y = kf(x) results in the parent function being vertically compressed when k = 1/2. Write the answer as a whole number of decimal
x y = kf(x) =___x^4
0 ___
1 ____
2 _____

Answer 1

Made mistake first part should have been f(x)=x^3
Second part should have been y =kf(x)=____x^4

Answer 2

To vertically stretch the parent function \( f(x) = x^2 \) by a factor of 3, we can express this as follows:

\[
y = kf(x) = 3x^2
\]

Now, we can complete the table for \( y = 3f(x) \):

### Table for \( y = 3x^2 \)
| x | y = 3f(x) = 3x^2 |
|-----|----------------------|
| 0 | 3(0^2) = 0 |
| 1 | 3(1^2) = 3 |
| 2 | 3(2^2) = 12 |

Now, we move onto the next part of your request, which involves vertically compressing the parent function \( f(x) = x^2 \) when \( k = \frac{1}{2} \):

\[
y = kf(x) = \frac{1}{2}x^2
\]

Now, we can complete the table for \( y = \frac{1}{2}x^2 \):

### Table for \( y = \frac{1}{2}x^2 \)
| x | y = \frac{1}{2}f(x) = \frac{1}{2}x^2 |
|-----|------------------------------------------|
| 0 | \(\frac{1}{2}(0^2) = 0\) |
| 1 | \(\frac{1}{2}(1^2) = \frac{1}{2} = 0.5\) |
| 2 | \(\frac{1}{2}(2^2) = \frac{1}{2}(4) = 2\) |

### Summary of Both Tables

1. **Vertical Stretch by 3:**
- When \( y = 3x^2 \):
- \( x = 0 \), \( y = 0 \)
- \( x = 1 \), \( y = 3 \)
- \( x = 2 \), \( y = 12 \)

2. **Vertical Compression by \( \frac{1}{2} \):**
- When \( y = \frac{1}{2}x^2 \):
- \( x = 0 \), \( y = 0 \)
- \( x = 1 \), \( y = 0.5 \)
- \( x = 2 \), \( y = 2 \)

Feel free to ask if you need any further clarification or assistance!

Answer 3

No problem! Let's correct that.

### Part 1: Vertical Stretch of \( f(x) = x^3 \) by a Factor of 3

To vertically stretch the function \( f(x) = x^3 \) by a factor of 3, we express this as:

\[
y = kf(x) = 3x^3
\]

Now, we can complete the table for \( y = 3x^3 \):

### Table for \( y = 3x^3 \)
| x | y = 3f(x) = 3x^3 |
|-----|----------------------|
| 0 | \(3(0^3) = 0\) |
| 1 | \(3(1^3) = 3\) |
| 2 | \(3(2^3) = 24\) |

### Part 2: Vertical Compression of \( f(x) = x^4 \)

Now, for the second part, to vertically compress the function \( f(x) = x^4 \) when \( k = \frac{1}{2} \):

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

Now, we can complete the table for \( y = \frac{1}{2}x^4 \):

### Table for \( y = \frac{1}{2}x^4 \)
| x | y = \frac{1}{2}f(x) = \frac{1}{2}x^4 |
|-----|------------------------------------------|
| 0 | \(\frac{1}{2}(0^4) = 0\) |
| 1 | \(\frac{1}{2}(1^4) = \frac{1}{2} = 0.5\) |
| 2 | \(\frac{1}{2}(2^4) = \frac{1}{2}(16) = 8\) |

### Summary of Both Tables

1. **Vertical Stretch of \( f(x) = x^3 \):**
- When \( y = 3x^3 \):
- \( x = 0 \), \( y = 0 \)
- \( x = 1 \), \( y = 3 \)
- \( x = 2 \), \( y = 24 \)

2. **Vertical Compression of \( f(x) = x^4 \):**
- When \( y = \frac{1}{2}x^4 \):
- \( x = 0 \), \( y = 0 \)
- \( x = 1 \), \( y = 0.5 \)
- \( x = 2 \), \( y = 8 \)

If you have any more questions or need further assistance, feel free to ask!