To two decimal places, find the value of k that will make the function f(x) continuous everywhere. f of x equals the quantity 3x + k for x less than or equal to -4 and is equal to kx^2 - 5 for x greater than -4 11.00 -2.47 -0.47 none of these

Given function is

now we need to find the value of k such that function f(x) continuous everywhere.

We know that any function f(x) is continuous at point x=a if left hand limit and right hand limits at the point x=a are equal.

So we just need to find both left and right hand limits then set equal to each other to find the value of k

To find the left hand limit (LHD) we plug x=-4 into 3x+k

so LHD= 3(-4)+k

To find the Right hand limit (RHD) we plug x=-4 into

so RHD=

Now set both equal

k=-0.47

Hence final answer is -0.47.

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step-by-step explanation: