Question

Let f(x)=−x²/2. If the graph of f(x) is translated 2 units up and 3 units left and the resulting graph is that of g(x), then g(1/2)= a. 0 b. -1/8 c. -2/8 d. -33/8 e. 13/8

Answer 1

To find g(1/2), we substitute x = 1/2 into the translated function g(x) and simplify. The correct answer is d. -33/8.

Step-by-step explanation:

To translate the graph of a function, we need to add or subtract values to the original function. Let's use the function f(x) = -x²/2 as given. To translate the function 2 units up, we add 2 to the function. To translate the function 3 units left, we subtract 3 from the x-value. So the translated function g(x) = -[(x + 3)²/2] + 2.

To find g(1/2), we substitute x = 1/2 into the function g(x) and simplify:

g(1/2) = -[(1/2 + 3)²/2] + 2

g(1/2) = -[(7/2)²/2] + 2

g(1/2) = -[49/8] + 2

g(1/2) = -49/8 + 16/8

g(1/2) = -33/8

Therefore, g(1/2) is -33/8. So the correct answer is d. -33/8.

Learn more about Function Translation