# continuous function

• August 9th 2009, 07:20 AM
live_laugh_luv27
continuous function
Find a value for a so that the function

$f(x) = \{2x-5, x<2$
$ax^2, x\ge2$

is continuous. I came up with the answer -1/4, but not sure how, or if it is correct.
Thanks!
• August 9th 2009, 07:50 AM
Plato
If x is near 2 but less than 2, $x \approx 2\;\& \,x < 2$, then $2x - 5 \approx - 1$.

If x is near 2 but greater than 2, $x \approx 2\;\& \,x > 2$, then we must have $ax^2 \approx - 1$. Therefore $a=\frac{-1}{4}$