Question

question for the function f(x) shown below, determine lim_{x→ - 4^{-}}f(x). f(x) = {10 - x^{2} for x > - 4; x - 1 for x < - 4} answer attempt 1 out of 2 dne

Explanation:

Step1: Identify the correct - part of the function

The notation $\lim_{x
ightarrow - 4^{-}}f(x)$ means the left - hand limit as $x$ approaches $-4$. For left - hand limit, we use the part of the function where $x < - 4$. The function for $x < - 4$ is $f(x)=x - 1$.

Step2: Substitute the value of $x$

We substitute $x=-4$ into the function $f(x)=x - 1$. So, $\lim_{x
ightarrow - 4^{-}}f(x)=\lim_{x
ightarrow - 4^{-}}(x - 1)$.
Using the direct substitution property of limits for polynomial functions, we get $(-4)-1$.

Step3: Calculate the result

$(-4)-1=-5$.

Answer:

$-5$