Question

A function h is defined by h(x)=x²+2x+4. Find the range of h corresponding to the domain (x less than or equal to -4 and x is less than or equal to 4).

A. h(x) ≤ 12
B. h(x) ≥ 4
C. h(x) ≤ 4
D. h(x) ≥ 12

Answer 1

The range of the function h(x) = x^2 + 2x + 4, corresponding to the given domain is h(x) ≥ 12.

Step-by-step explanation:

The function h(x) is defined as h(x) = x2 + 2x + 4.

To find the range of h corresponding to the given domain (x ≤ -4 and x ≤ 4), we need to determine the minimum and maximum values of h within this domain.

To find the minimum value, we evaluate h(x) at x = -4, which gives:

h(-4) = (-4)2 + 2(-4) + 4 = 16 - 8 + 4 = 12.

To find the maximum value, we evaluate h(x) at x = 4:

h(4) = (4)2 + 2(4) + 4 = 16 + 8 + 4 = 28.

Therefore, the range of h for the given domain is h(x) ≥ 12 and h(x) ≤ 28. From the available options, the correct answer is D. h(x) ≥ 12