Question

What is the range of this function?

Function: f(x) = 1/2⋅x^2 + 4
Domain(x): {-2, 0, 4}
a) {0, 2, 8}
b) {4, 6, 10}
c) {4, 5, 8}
d) {4, 8, 12}

Answer 1

The range of the function f(x) = 1/2⋅x^2 + 4 for the domain {-2, 0, 4} is calculated as {4, 6, 12}, corresponding to option D.

Step-by-step explanation:

The question asks to find the range of the function f(x) = 1/2⋅x^2 + 4 for the given domain {-2, 0, 4}. To find the range, we calculate the function values at each point in the domain and use these values to determine the set of possible outputs (the range).

• For x = -2: f(-2) = 1/2⋅(-2)^2 + 4 = 1/2⋅ 4 + 4 = 2 + 4 = 6
• For x = 0: f(0) = 1/2⋅ 0^2 + 4 = 0 + 4 = 4
• For x = 4: f(4) = 1/2⋅ 4^2 + 4 = 1/2⋅ 16 + 4 = 8 + 4 = 12

Therefore, the range of f(x) for the given domain is {4, 6, 12}, which corresponds to option D.