Which of the following tables shows that y=kf(x)

Question

Which of the following tables shows that y=kf(x)
 results in the parent function y=|x+4|
 being vertically stretched by a k factor of 3?(1 point)
Responses

x	y=kf(x)
0	4
1	5
2	6
  x y equals k f left parenthesis x right parenthesis 0 4 1 5 2 6

x	y=kf(x)
0	1.3
1	1.7
2	2
  x y equals k f left parenthesis x right parenthesis 0 1.3 1 1.7 2 2

x	y=kf(x)
0	12
1	15
2	18
x y equals k f left parenthesis x right parenthesis 0 12 1 15 2 18

x	y=kf(x)
0	−12
1	−15
2	−18
    x y equals k f left parenthesis x right parenthesis 0 negative 12 1 negative 15 2 negative 18
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GPT-4o mini · Answer

To determine which table shows that $ y = kf(x) $ results in the parent function $ y = |x + 4| $ being vertically stretched by a factor of $ k = 3 $, we first need to find the values of $ f(x) $. The parent function is $ f(x) = |x + 4| $. Let's calculate $ f(x) $ for the values of $ x $ in the tables provided: 1. For $ x = 0 $: $$ f(0) = |0 + 4| = 4 $$ 2. For $ x = 1 $: $$ f(1) = |1 + 4| = 5 $$ 3. For $ x = 2 $: $$ f(2) = |2 + 4| = 6 $$ When $ y = kf(x) $ and $ k = 3 $, we have: - For $ x = 0 $: $ y = 3 \cdot 4 = 12 $ - For $ x = 1 $: $ y = 3 \cdot 5 = 15 $ - For $ x = 2 $: $ y = 3 \cdot 6 = 18 $ Thus, the matching table would yield: $$ \begin{aligned} x & \quad y = kf(x) \ 0 & \quad 12 \ 1 & \quad 15 \ 2 & \quad 18 \ \end{aligned} $$ Looking at the options provided, the correct table is: $$ x \quad y = kf(x) \ 0 \quad 12 \ 1 \quad 15 \ 2 \quad 18 $$ So the correct response is the third table: - $ x = 0 $, $ y = 12 $ - $ x = 1 $, $ y = 15 $ - $ x = 2 $, $ y = 18 $