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

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!

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!