Question

question 15 find the value of k which makes the following piecewise function continuous for all values of x. \\( f(x) = \

$$\begin{cases} -3, & \\text{if } x < 2 \\\\ k - 5x, & \\text{if } x \\geq 2 \\end{cases}$$

\\) options: 4, 7, 8, 5, 3

Explanation:

Step1: Set equal at $x=2$

For continuity, $f(2^-) = f(2^+)$

Step2: Compute left-hand limit

$f(2^-) = -3$

Step3: Compute right-hand limit

$f(2^+) = k - 5(2) = k - 10$

Step4: Solve for $k$

Set $-3 = k - 10$
$k = 10 - 3 = 7$

Answer:

B. 7