SOLUTION: Consider the function below. lim x -> 3 (2x+1)=7 What values of x guarantee that f(x)=2x+1 is within 0.54 units of 7? If x is within _____ units of 3, then f(x) is within 0.54

Algebra ->  Test -> SOLUTION: Consider the function below. lim x -> 3 (2x+1)=7 What values of x guarantee that f(x)=2x+1 is within 0.54 units of 7? If x is within _____ units of 3, then f(x) is within 0.54       Log On


   

Question 1120558: Consider the function below. lim x -> 3 (2x+1)=7
What values of x guarantee that f(x)=2x+1 is within 0.54 units of 7?
If x is within _____ units of 3, then f(x) is within 0.54 units of 7.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


We need to have
7-0.54 < 2x+1 < 7+0.54
6.46 < 2x+1 < 7.54
5.46 < 2x < 6.54
2.73 < x < 3.27

Since this is a linear function, the upper and lower limits are the same distance of 0.27 from 3.

So to guarantee that 2x+1 is within 0.54 units of 7, x has to be within 0.27 units of 3.

The preceding is a formal process for finding the solution. Since this is a linear function with a slope of 2, it should be obvious that x needs to be within 0.27 units of 3 for f(x) to be within 0.54 units of 7.