Find the value for k so that the function will be continuous at x=4𝑥=4.f(x)=−8x2+64x−128x−4−73x2+24x+48+kifx<4ifx≥4

Question

Find the value for k so that the function will be continuous at x=4

f(x) =
$\begin{cases} -8x^2 + 64x - 128 & \text{if } x < 4 \\ -73x^2 + 24x + 48 + k & \text{if } x \geq 4 \end{cases}$

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Solution

To find the value of k that makes the function continuous at x=4, we need to set the two pieces of the function equal to each other at x=4 and solve for k.

First, plug x=4 into the first function:

-8*(4)^2 + 644 - 128 = -816 + 256 - 128 = -128 + 256 - 128 = 0

Then, plug x=4 into the second function:

-73*(4)^2 + 244 + 48 + k = -7316 + 96 + 48 + k = -1168 + 96 + 48 + k = -1024 + k

Setting these two equal to each other gives:

0 = -1024 + k

Solving for k gives:

k = 1024

This problem has been solved

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Find the value for k so that the function will be continuous at x=4𝑥=4.f(x)=−8x2+64x−128x−4−73x2+24x+48+kifx<4ifx≥4

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