how do you write an equation for the linear function f with the given values?
Standard linear function is f(x)=ax+b where a and b are constants.
Substitute each point into the function:
21=-2a+b, -35=5a+b. We need go no further because we have two linear equations and two unknowns.
f(-2)-f(5): 56=-7a so a=-8. Now we can work out b: b=21+2a=21-16=5 so f(x)=5-8x.
Quick check shows that the function is correct: f(-2)=5+16=21; f(5)=5-40=-35.
But we need to check all the other points:
f(-6)=5+48=53; f(3)=5-24=-19; uh-oh, something wrong!
The values don't fit. So either f(x) is not linear or it's piecewise.
Closer inspection is needed. First plot the points. It's clear to see that the points are not colinear. Join the points with straight lines. We're not told that f is continuous. Let's assume it is. If it's piecewise, we need 5 different equations to define the function between the 6 points. In order these are (-9,-4), (-6,-2), (-2,21), (3,-5), (5,-35), (12,14). Call these points A, B, C, D, E, F. We can work out linear equations between A and B, B and C, C and D, etc. These equations will provide continuity for f in the domain -9 Read More: ...