started: apr 6 at 6:36pm quiz instructions show instructions question 5 6 pts provide an response. is the…

Explanation:

Step1: Find the left - hand limit

We find $\lim_{x\rightarrow1^{-}}f(x)$. Since $x\rightarrow1^{-}$ means $x < 1$, we use $f(x)=-4x - 3$. $\lim_{x\rightarrow1^{-}}(-4x - 3)=-4\times1-3=-7$

Step2: Find the right - hand limit

We find $\lim_{x\rightarrow1^{+}}f(x)$. Since $x\rightarrow1^{+}$ means $x>1$, we use $f(x)=2x - 4$. $\lim_{x\rightarrow1^{+}}(2x - 4)=2\times1-4=-2$

Step3: Check the value of the function at $x = 1$

Since $x = 1$ satisfies $x\leq1$, $f(1)=-4\times1-3=-7$

Step4: Check the continuity condition

For a function to be continuous at $x = a$, $\lim_{x\rightarrow a^{-}}f(x)=\lim_{x\rightarrow a^{+}}f(x)=f(a)$. Here, $\lim_{x\rightarrow1^{-}}f(x)=-7$, $\lim_{x\rightarrow1^{+}}f(x)=-2$ and $f(1)=-7$. Since $\lim_{x\rightarrow1^{-}}f(x)\neq\lim_{x\rightarrow1^{+}}f(x)$, the function is not continuous at $x = 1$.

Answer:

The function $f(x)$ is not continuous at $x = 1$ because $\lim_{x\rightarrow1^{-}}f(x)=-7$ and $\lim_{x\rightarrow1^{+}}f(x)=-2$, and the left - hand limit is not equal to the right - hand limit.