Question

Which statement describes the end behavior of this function?

g(x)= 1/2 |x– 3|– 7
A. As x approaches negative infinity, g(x) is no longer continuous.
B. As x approaches positive infinity, g(x) approaches negative infinity.
C. As x approaches positive infinity, g(x) approaches positive infinity.
D. As x approaches negative infinity, g(x) approaches negative infinity.

Answer 1

The end behavior of the function g(x) = 1/2 |x - 3| - 7 is that as x approaches negative infinity, g(x) approaches negative infinity.

Step-by-step explanation:

The end behavior of the function g(x) = 1/2 |x - 3| - 7 can be determined by looking at the leading term of the function, which is |x - 3|. The absolute value function |x - 3| represents the distance between x and 3, and it will always be positive or zero. Multiplying it by 1/2 will not change its behavior.

Therefore, as x approaches negative infinity (x → -∞), |x - 3| will approach positive infinity, and g(x) will approach negative infinity.

So, the correct statement describing the end behavior of g(x) is D. As x approaches negative infinity, g(x) approaches negative infinity.