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## Homework Statement

Find the values of 'a' and 'b' that make f(x) a continuous function.

f(x) =

x+4, x≤-1

ax+bx, -1<x<3

3x+2, x≥3

## Homework Equations

None

## The Attempt at a Solution

I plugged -1 and 3 into their respective functions to get the points: (-1,3) and (3,11)

(-1)+4=3

3(3)+2=11

Found the slope between those two points: m=2, otherwise known as 'a'

m=(11-3)/(3-(-1))=2 ---> a

Plugged that into the point-slope formula using the point (-1,3)

y-3=2(x+1)

Solved it for b:

y-3=2x+2

y=2x+5 -----> y=mx+b so 5 is 'b'

a=2 b=5

Line that fills the gap or jump between other two equations is: y=2x+5

I even graphed it to make sure and that is the equation of the line that would fill the gap between (x+4) and (3x+2) but if you plug the values of 'a' and 'b' into the original equation, it isn't right and doesn't make sense:

ax+bx ----> 2x+5x ----> f(x)=7x to make it continues, which is wrong

I don't understand the +bx part of the ax+bx