Here are the answers to each question based on the information provided:
Question 1 A) The table that shows that \( y = kf(x) \) results in the parent function \( y = |x + 4| \) being vertically stretched by a k factor of 3, would be:
- \( x, y = kf(x) \)
0, 12
1, 15
2, 18
This is because the values in the second table are those of the absolute function multiplied by 3:
For \( f(x) = |x + 4| \):
- \( f(0) = |0 + 4| = 4 \) thus \( y = 3f(0) = 34 = 12 \)
- \( f(1) = |1 + 4| = 5 \) thus \( y = 3f(1) = 35 = 15 \)
- \( f(2) = |2 + 4| = 6 \) thus \( y = 3f(2) = 36 = 18 \)
Answer:
x, y = kf(x)
0, 12
1, 15
2, 18
Question 2 A) The statement that describes the transformed function \( y = 4f(x) \):
- The parent function has been vertically stretched by a factor of 4.
Answer:
The parent function has been vertically stretched by a factor of 4.
Question 3 A) The factor \( k \) for the vertical compression from the function \( f(x) = x^3 + 2 \) to the function \( f(x) = \frac{1}{4}x^3 + 12 \):
- \( k = \frac{1}{4} \), since it is a compression.
Answer:
k = \frac{1}{4}
Question 4
A) The original function \( y = 12x - 4 \) to find the x-intercepts:
To find the x-intercept, set \( y = 0 \):
\( 0 = 12x - 4 \rightarrow 12x = 4 \rightarrow x = \frac{4}{12} = \frac{1}{3} \)
For the vertically dilated function \( y = 6(12x - 4) = 72x - 24 \):
Set \( y = 0 \):
\( 0 = 72x - 24 \rightarrow 72x = 24 \rightarrow x = \frac{24}{72} = \frac{1}{3} \)
Thus, both functions have the same x-intercept.
Answer:
The original function has an x-intercept of \( ( \frac{1}{3}, 0 ) \), and the dilated function has an x-intercept of \( ( \frac{1}{3}, 0 ) \).
Question 5 A) Both graphs represent transformations:
- Both graphs represent vertical stretches, although they use different factors of k.
Answer:
Both graphs represent vertical stretches, although they use different factors of k.
If you have any further questions or need clarifications, feel free to ask!
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