Final answer:
The values of the function h(x) = x² - 5x + 7 at the given points are: 1) h(2) = 1, 2) h(-5) = 57, and 3) 1/3 x h(-8) = 37.
Step-by-step explanation:
The student has provided a function h(x) = x² - 5x + 7 and asks for evaluations at different values of x. To solve this, we will substitute the given values into the function and perform the necessary arithmetic operations.
- h(2): We substitute 2 into the function: (2)² - 5(2) + 7 = 4 - 10 + 7 = 1.
- h(-5): We substitute -5 into the function: (-5)² - 5(-5) + 7 = 25 + 25 + 7 = 57.
- 1/3 x h(-8): First calculate h(-8): (-8)² - 5(-8) + 7 = 64 + 40 + 7 = 111. Then multiply by 1/3: 1/3 x 111 = 37.
Through these calculations, we find the values of the function h(x) at specific points, which is a common task in understanding the behavior of functions in mathematics.