Question

find the value of the constant m that makes f(x) continuous

http://webwork.math.ttu.edu/wwtmp/equations/3a/d348f323a2288183c0a6f7dd24d3ce1.png

Answer 1

well, we know they have to equal at -3

Answer 2

so thats what would tell us that it is in fact continuous?

Answer 3

yes

Answer 4

solve the bottom for "x" and use that to calibrate for m

Answer 5

well i factored and got x = 1 and -5
neither of those led me to -3 in the top equ

Answer 6

x^2+4x-5 = -3

x^2 +4x -2 = 0

x^2 +4x+4 -4 -2 = 0

(x+2)^2 = 6

x = -2 +- sqrt(6) it looks like

dbl chk that so far

Answer 7

ok so you set it = -3

Answer 8

yes, -3 is the spot that we need contiuity at; it tells us that at -3 we have a pieced function to glue together

Answer 9

i might be thinking a little to much into it tho

Answer 10

when x=-3, what the value we get from the bottm

Answer 11

thats better

Answer 12

so i can just plug -3 into x?

Answer 13

yes, since it says x=-3 we need to know that value at x=-3 ; i was someplace else to begin with

Answer 14

m(-3) -8 = that value

Answer 15

personally i think m=0 at the moment

Answer 16

well i plugged it in and m=0 is correct but I'm not sure how

Answer 17

all together we get:

m(-3) - 8 = (-3^2) +4(-3) - 5

and solve for m :)

Answer 18

ok so can you do this for any set of two equations like this or is this a special case. Im referring to setting them equal to each other

Answer 19

setting them equal to each other assures that they results will be continuous at the offending point.

Answer 20

there might be other tricks that have to be done along the way, but essentially that is the idea