Question

When the function -5|x + 7| + 8 is translated 3 units left, it gives another function g(x). Choose the correct form of g(x).

A. -5|x + 4| + 8
B. -5|x + 10| + 8
C. -5|x + 7| + 11
D. -5|x + 7| + 5

Answer 1

The correct function g(x) when the original function is translated 3 units to the left is -5|x + 10| + 8, represented by option B.

Step-by-step explanation:

To find the correct form of function g(x) when the original function -5|x + 7| + 8 is translated 3 units to the left, we need to adjust the expression inside the absolute value. In algebra, translating a function to the left by 'd' units is represented by adding 'd' to the x value inside the function. Therefore, to translate this function by 3 units to the left, the correct transformation is:

-5|x + 7| + 8 → -5|x + (7 + 3)| + 8

Simplifying the expression within parentheses gives us:

-5|x + 10| + 8

Hence, the correct form of g(x) is -5|x + 10| + 8, which is represented by option B in the question.