Question

Find the value of constants c and d that make the function below continuous at
x = 2.
x^2-3x x<2
F(x) c x=2

Answer 1

whoops...and d+x x>2 is the last part

Answer 2

For it to be continuous, the values of each function would have to be equal at 2. In mathematical terms:
\[x^2-3x = c = d+x\]

Answer 3

so like x^2-3x=d+x=2?

Answer 4

They don't equal 2 I'm afraid. Take the first expression for example:
\(f(x) = x^2-3x\)
What would f(x) equal at x=2?

Answer 5

no it would at 3 though?

Answer 6

I mean what is f(2)?

Answer 7

-2?

Answer 8

Correct! Now going back to the equation I wrote earlier:
\[x^2-3x = c = d+x \text{ ; } x=2\]You should be able to work out the values of c and d.