To show that the transformation \( y = k f(x) \) results in the parent function \( y = x + 4 \) being vertically stretched by a factor of \( k = 3 \), we will first define the transformation correctly and then evaluate it for the given \( x \)-values.
The parent function is given as:
\[ f(x) = x + 4 \]
If we want to vertically stretch this function by a factor of \( k = 3 \), we will apply the transformation:
\[ y = k f(x) = 3 (x + 4) \]
Next, we can simplify this expression:
\[ y = 3x + 12 \]
Now, we’ll compute the values of \( y \) for the provided \( x \)-values (0, 1, 2):
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For \( x = 0 \): \[ y = 3(0) + 12 = 12 \]
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For \( x = 1 \): \[ y = 3(1) + 12 = 3 + 12 = 15 \]
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For \( x = 2 \): \[ y = 3(2) + 12 = 6 + 12 = 18 \]
So, the resulting values can now be compiled into a table:
| \( x \) | \( y \) | |:-----:|:-----:| | 0 | 12 | | 1 | 15 | | 2 | 18 |
This table shows the transformed values for the function \( y = 3(x + 4) \) or \( y = 3x + 12 \), demonstrating that the function has been vertically stretched by a factor of 3.