Question

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

Explanation:

Step1: Identify vertical reflection

Notice that $j(x)$ is a downward-opening curve, and $k(x)$ is an upward-opening curve, which means $k(x)$ is the vertical reflection of $j(x)$. A vertical reflection of a function $f(x)$ is $-f(x)$.

Step2: Verify with key points

Take the vertex of $j(x)$ (on the y-axis, lower point) and $k(x)$ (on the y-axis, upper matching point): if $j(x)$ has a point $(0, a)$ where $a<0$, $k(x)$ has $(0, -a)$, which fits $k(x) = -j(x)$. Also, for other symmetric points, the y-values of $k(x)$ are the negative of $j(x)$'s y-values.

Answer:

$-j(x)$