Question

For what value of k is the function f(x)={kx+5, x>4} {x^2 -x, x< or =4} , continuous? JYA

Answer 1

Find the value of x^2 - x when x=4...
4^2 - 4 = 12

Now find what kx+5 is equal to when x=4...
4k+5

For the function to be continuous: the value of kx+5 (when x=4) must equal the value of x^2 - x (when x=4)

So since they're equal, solve this for k:

4k+5 = 12

Answer 2

you're a genius. why didn't i think of that? thank you

Answer 3

No prob :)

Answer 4

so k would equal 7/4? @agent0smith

Answer 5

It would.

Answer 6

thank you so much

Answer 7

Then you can graph them to see that they're continuous: https://www.google.com/search?q=x%5E2+-x&oq=x%5E2+-x&aqs=chrome..69i57&sourceid=chrome&ie=UTF-8#q=x%5E2-x%2C+7%2F4x%2B5&safe=off

Where x=4, the two lines intersect, so the original function f(x)={kx+5, x>4} {x^2 -x, x< or =4} is continuous

Answer 8

no i just needed to know how to do it because im finishing up a math test remediation lol ive got more problems to do:)

Answer 9

i just wasn't sure how to go about that one