Question

Write a linear function f with values f(-3) = 5 and f(6) = 11.

a) f(x) = (2/3)x + 7
b) f(x) = (3/2)x + 7
c) f(x) = (2/3)x + 11
d) f(x) = (3/2)x + 5

Answer 1

The correct linear function is option a) f(x) = (2/3)x + 7, as it is the only function provided that satisfies the given conditions f(-3) = 5 and f(6) = 11.

Step-by-step explanation:

To determine which function, f(x), satisfies the given conditions, we must ensure that the function passes through the points (-3, 5) and (6, 11). We can plug these x-values into the potential functions to see which one gives us the correct y-values.

• For option a) f(x) = (2/3)x + 7:
• For option b) f(x) = (3/2)x + 7, those conditions are not satisfied.
• For option c) f(x) = (2/3)x + 11, those conditions are not satisfied.
• For option d) f(x) = (3/2)x + 5, those conditions are not satisfied.

Therefore, the correct equation is option a) f(x) = (2/3)x + 7, which satisfies both conditions f(-3) = 5 and f(6) = 11.