Find the values of 'a' and 'b' that make f(x) a continuous function.
The Attempt at a Solution
I plugged -1 and 3 into their respective functions to get the points: (-1,3) and (3,11)
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)
Solved it for b:
y=2x+5 -----> y=mx+b so 5 is 'b'
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