Mathematics, 18.01.2021 08:00 chaanah

If you could help I would really appreciate it, but if not that’s fine. Thank you.

Answers: 2

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Answer from: mmelody5

Option C is correct answer.

Step-by-step explanation:

We need to draw the graph of piece wise function

$f(x)\[ \begin{cases} -2-x & if\:x\leq 1 \\ -3+2x & if\: x1 \end{cases}\]$

So, for drawing the graph, we will find values of f(x) for both the given equations.

First finding f(x) for $-2-x \:\: if\:x\leq1$

The value of x must be less than or equal 1

x f(x)

1 -3

0 -2

-1 -1

-2 0

-3 1

-4 2

The graph will start from closed circle because x ≤ 1

Now, finding values of f(x) for $-3+2x\: if\:x1$

The value of x must be greater than 1

x f(x)

2 1

3 3

4 5

5 7

The graph will start from open circle because x> 1

Now, plotting these numbers we will get graph of Option C.

Option C is correct answer.

Answer from: Quest

2 5/8 is the final answer! : )

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

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