Value of a constant that makes a function continuous.

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bktheking

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Feb 12, 2012
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Having some trouble with this problem:
Find the value of the constant k that makes the function continuous. If x cannot = 3, h(x) = (4x2 + 9x -9)/x+3. If x = 3, h(x) = (4x+k)

Here's how I went about it:
Factoring (4x2 + 9x -9) gives (4x-3)(x+3).
The (x+3) in the denominator cancels the (x+3) factored, leaving (4x-3).
Setting (4x-3) equal to (4x+k) and subistuting -3 for x gives k=-3.
However, this answer is marked wrong. Any ideas on what I'm doing wrong?
 
tkhunny said:
That makes no sense, but does not change your correct solution.
Click to expand...
Sorry, " If x cannot = 3, h(x) = (4x2 + 9x -9)/x+3. If x = 3, h(x) = (4x+k)"should read " If x cannot = -3, h(x) = (4x2 + 9x -9)/x+3. If x = -3, h(x) = (4x+k)" That's why I substituted -3 for x. Still haven't figured this out.
 
What is the limit, L, as x goes to -3 of h(x)?

Pick k so that the limit as x goes to -3 of (4x+k) is equal to L.

Finally, verify that h(-3)=L.

This all becomes obvious if you factor 4x^2+9x-9.
 
It would help if you would write either "3" or "-3" on each occasion. Switching back and forth doesn't work.
 
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