type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction…

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s). the graph represents the piece - wise function: $f(x)=\begin{cases}square,\text{ if } - 3leq xlt - 1\\square,\text{ if } - 1leq xleq1end{cases}$

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s). the graph represents the piece - wise function: $f(x)=\begin{cases}square,\text{ if } - 3leq xlt - 1\\square,\text{ if } - 1leq xleq1end{cases}$

Answer

Explanation:

Step1: Find the function for -3 ≤ x < -1

For -3 ≤ x < -1, we use the two - point form of a line $y - y_1=\frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$. The two points on the line are (-3,1) and (-1,2). First, calculate the slope $m=\frac{2 - 1}{-1-(-3)}=\frac{1}{2}$. Using the point - slope form with the point (-3,1), we have $y - 1=\frac{1}{2}(x + 3)$, which simplifies to $y=\frac{1}{2}x+\frac{3}{2}+1=\frac{1}{2}x+\frac{5}{2}$.

Step2: Find the function for -1 ≤ x ≤ 1

For -1 ≤ x ≤ 1, the line is horizontal. The y - value is 5 for all x in the interval [-1,1]. So the function is $y = 5$.

Answer:

$\frac{1}{2}x+\frac{5}{2}$, $5$