suppose that the function (f) is defined, for all real numbers, as follows.\nf(x)=\begin{cases}x…

suppose that the function (f) is defined, for all real numbers, as follows.\nf(x)=\begin{cases}x - 4&\text{if }x<2\\-2x + 2&\text{if }xgeq2end{cases}\ngraph the function (f). then determine whether or not the function is continuous.\nis the function continuous?\nyes\nno

suppose that the function (f) is defined, for all real numbers, as follows.\nf(x)=\begin{cases}x - 4&\text{if }x<2\\-2x + 2&\text{if }xgeq2end{cases}\ngraph the function (f). then determine whether or not the function is continuous.\nis the function continuous?\nyes\nno

Answer

Explanation:

Step1: Find the left - hand limit as x approaches 2

We use the part of the function for (x < 2), (f(x)=x - 4). (\lim_{x\rightarrow2^{-}}f(x)=\lim_{x\rightarrow2^{-}}(x - 4)=2-4=- 2)

Step2: Find the right - hand limit as x approaches 2

We use the part of the function for (x\geq2), (f(x)=-2x + 2). (\lim_{x\rightarrow2^{+}}f(x)=\lim_{x\rightarrow2^{+}}(-2x + 2)=-2\times2+2=-2)

Step3: Find the value of the function at x = 2

We use the part of the function for (x\geq2), (f(2)=-2\times2 + 2=-2) Since (\lim_{x\rightarrow2^{-}}f(x)=\lim_{x\rightarrow2^{+}}f(x)=f(2)=-2), the function is continuous.

Answer:

Yes