SOLUTION: Piecewise function. f(x)={x+4, x ≥ 2 and ax^2, x < 2 A. Find the value for "a" so that f(x) is continuous for all real numbers. B. Sketch the graph to verify results fr

Question 1021099: Piecewise function.
f(x)={x+4, x ≥ 2 and ax^2, x < 2
A. Find the value for "a" so that f(x) is continuous for all real numbers.
B. Sketch the graph to verify results from part A.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

For any value of

where

regardless of the value of

. There are a couple of basic limit theorems that you can apply to the segments of this function where

, and I'll leave that part of the analysis to you.

Therefore, for this piecewise fuction to be continuous for all reals, it is sufficient to find a number

such that

when

And the desired function is:

John

My calculator said it, I believe it, that settles it

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SOLUTION: Piecewise function. f(x)={x+4, x &#8805; 2 and ax^2, x < 2 A. Find the value for "a" so that f(x) is continuous for all real numbers. B. Sketch the graph to verify results fr

SOLUTION: Piecewise function. f(x)={x+4, x ≥ 2 and ax^2, x < 2 A. Find the value for "a" so that f(x) is continuous for all real numbers. B. Sketch the graph to verify results fr