What values of x guarantee that f(x) = 4x - 3 is within 1 unit of 5?

Question

Consider the function below.

What values of x guarantee that f(x) = 4x - 3 is within 1 unit of 5?

Select one:

a. If x is within 2.25 units distance of 2, then f(x) is within 1 unit of 5.

b. If x is within 1.75 units distance of 2, then f(x) is within 1 unit of 5.

c. If x is within 0.25 unit distance of 2, then f(x) is within 1 unit of 5.

d. If x is within 2 units distance of 2, then f(x) is within 1 unit of 5.

Answer 1

Let h be the variation in x=2, then the corresponding variation in f(x) has to be between 5±1. Let k be the variation in 5, so 4(2+h)-3=5+k, and we solve for h: 8+4h-3=5+k. So 4h=k and k=1 (given), therefore h=k/4=1/4=0.25. Answer c.