Question

Find the value of k that will make the function continuous.
f(x)=3x+k x≤-4
f(x)=kx^2-5 x>-4

Answer 1

you want the function to be continuous everywhere
but we are having a small issues at x=-4

We want the left limit equal to the right limit as x approaches -4.

Answer 2

So set up that equation and solve for k.

Answer 3

Would k=3x-5?

Answer 4

did you try to find the left limit and right limit of your function as x approaches -4 yet?

Answer 5

No not yet so I would have to plug both the equations into my calculator and find the limit as it approaches -4?

Answer 6

\[\lim_{x \rightarrow -4^+}f(x)=\lim_{x \rightarrow -4^-}f(x)\]
you don't need a calculator
you are just substituting the -4 into both sides of your function (since both functions are actually continuous at x=-4)

Answer 7

I got 12 and .3125 as values

Answer 8

so what do you get when you plug in -4 for x into 3x+k?
and what do you get when plug in -4 for x into kx^2-5?

Answer 9

how?

Answer 10

where did you get those?

Answer 11

When I plugged in -4 into 3x+k and solved for k I got 12. The same thing for the second one but I got .3125

Answer 12

I don't get what you are doing to get those values

when you plug in -4 for x into 3x+k you get -12+k
and when plug in -4 for x into kx^2-5 you get 16k-5
now you set left limit=right limit
and solve for k
-12+k=16k-5

Answer 13

I have to go but I think you can finish this now
that is just a linear equation

Answer 14

Okay thank you!