Question

Select the correct answer from each drop-down menu.

~look at picture~

The graph represents the piecewise function

Answer 1

The left line segment has slope 2 and includes the point (-1, -3). The right line segment has slope 1 and includes the point (1, 5). The function can be written as ...

$f(x)=\left\{\begin{array}{rcl}2x-1&\mbox{if}&x\le-1\\x+4&\mbox{if}&x\ge1\end{array}\right\,$

Answer 2

Answer:

$f(x)=\left\{\begin{matrix}2x-1,\ & x\leq -1\\ x+4,\ & x\geq 1\end{matrix}\right.$

Step-by-step explanation:

From the graph, we see that,

The function is divided with domain being $x\leq -1$ and $x\geq 1$.

The general form of a straight line is $y=mx+b$, where m= slope and b= y-intercept.

So, we have,

1. In the region when $x\leq -1$, the function passes through the points (-1,-3) and (-2,-5).

The slope is given by $m=\dfrac{-5+3}{-2+1}=\dfrac{-2}{-1}=2$

Substituting m= 2 and point (-1,-3) in the general form gives us,

$-3=2\times -1+b\\\\-3+2=b\\\\b=-1$

Thus, the equation of the line is $y=2x-1$.

2. In the region when $x\geq 1$, the function passes through the points (1,5) and (2,6).

The slope is given by $m=\dfrac{6-5}{2-1}=1$

Substituting m= 1 and point (1,5) in the general form gives us,

$5=1\times 1+b\\\\5-1=b\\\\b=4$

Thus, the equation of the line is $y=x+4$.

Hence, the piece wise function is given by $f(x)=\left\{\begin{matrix}2x-1,\ & x\leq -1\\ x+4,\ & x\geq 1\end{matrix}\right.$