For a function $g$ , the graph of $y=g(x)$ is shown. When $g(x)$ is divided by $(x+10)$ , the remainder is $-20$ . Which of the following is closest to the remainder when $g(x)$ is divided by $(x-10)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-28$ $\newline$ (B) $-2$ $\newline$ (C) $2$ $\newline$ (D) $28$

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Grade 8

Mean, median, mode, and range: find the missing number

Full solution

Q. For a function

g

, the graph of

y=g(x)

is shown. When

g(x)

is divided by

(x+10)

, the remainder is

-20

. Which of the following is closest to the remainder when

g(x)

is divided by

(x-10)

\newline

Choose

1

answer:

\newline

(A)

-28

\newline

(B)

-2

\newline

(C)

2

\newline

(D)

28

Given Information: We are given that when $g(x)$ is divided by $(x+10)$ , the remainder is $-20$ . This information suggests that $g(-10) = -20$ , because when a polynomial $g(x)$ is divided by a linear factor $(x - a)$ , the remainder is $g(a)$ .
Find Remainder for $x-10$ : To find the remainder when $g(x)$ is divided by $x-10$ , we need to evaluate $g(10)$ . However, we do not have the explicit function $g(x)$ or its graph provided. We can only make an approximation based on the given information.
Approximation Based on Given Info: Since we do not have the exact values or the graph, we cannot calculate the exact remainder when $g(x)$ is divided by $(x-10)$ . We can only guess that the remainder will be close to the given remainder of $-20$ when $g(x)$ was divided by $(x+10)$ , assuming that the behavior of $g(x)$ does not change drastically between $-10$ and $10$ .
Elimination of Options: Given the options (A) $-28$ , (B) $-2$ , (C) $2$ , and (D) $28$ , we can infer that the remainder when $g(x)$ is divided by $(x-10)$ is likely to be negative as well, since $g(-10)$ is negative and we are assuming a smooth behavior of $g(x)$ . Therefore, we can eliminate options (C) and (D).
Final Approximation: Between the remaining options (A) $-28$ and (B) $-2$ , without additional information, we cannot determine which one is closer to the actual remainder. However, if we assume that the change in the remainder is not too large when shifting from $(x+10)$ to $(x-10)$ , option (B) $-2$ seems too small a change from $-20$ . Therefore, option (A) $-28$ might be a more reasonable approximation.