Question

question 1 (2 points)
express k(x) in terms of j(x).
graph of j(x) and k(x) on a grid

k(x) =
blank 1:

question 2 (4 points)
g(x) is a transformation of f(x).

x	f(x)		x	g(x)
-1	0		-1	0
0	1		0	-1
1	8		1	-8
2	27		2	-27

describe the transformation

write the equation for g(x) in terms of f(x).
g(x) =
blank 1:
blank 2:

question 3 (1 point)
which equation describes b(x) as a transformation of a(x)?

Explanation:

Step1: Analyze Question1 graph transformation

Observe that $k(x)$ is a vertical reflection of $j(x)$ over the x-axis, meaning each $y$-value of $j(x)$ is multiplied by $-1$, and then shifted up. From the vertex: $j(x)$ has vertex at $(0, -8)$, $k(x)$ has vertex at $(0, 8)$. So $k(x) = -j(x) + 16$? No, wait: when $x=0$, $j(0)=-8$, $k(0)=8$. $-j(0) = 8$, which matches. Check another point: $j(3)=1$, $k(3)=-1$? No, wait no, looking at the graph: $j(x)$ is the downward opening, $k(x)$ upward. For any $x$, $k(x) = -j(x)$. Wait, $j(0) = -8$, $-j(0)=8$, which is $k(0)$. $j(4)=0$, $-j(4)=0$, which is $k(4)$. Yes, that fits.
$k(x) = -j(x)$

Step2: Analyze Question2 table values

Compare $f(x)$ and $g(x)$: for each $x$, $g(x) = -f(x)$. For $x=-2$, $f(-2)=-1$, $g(-2)=1=-(-1)$; $x=0$, $f(0)=1$, $g(0)=-1=-1$; $x=2$, $f(2)=27$, $g(2)=-27=-27$. This is a vertical reflection over the x-axis.

Step3: Write Question2 equation

Based on the reflection, $g(x) = -f(x)$

Answer:

Question 1: $k(x) = -j(x)$
Question 2:

• Description: Reflection over the x-axis
• $g(x) = -f(x)$

Question 3: (No options provided, cannot answer. Please share the options for Question 3 to complete the solution.)