Question

A piecewise function g(x) is represented by the graph. On a coordinate plane, a piecewise function has 3 lines. The first line has an open circle at (negative 2, negative 2) and it continues horizontally to (negative 5, negative 2). The second line has a closed circle at (negative 2, 0) and then continues up to an open circle at (1, 1.5). The third line has a closed circle at (1, 4) and continues down to (5, negative 4). Which functions represent a piece of the function? Select three options. g(x) = −2x, −2 < x < 0 g(x) = −2, x < −2 g(x) = x − 2, −2 < x < 1 g(x) = −2x + 6, x ≥ 1 g(x) = + 1, –2 ≤ x < 1

Answer 1

Answer:

see the explanation

Step-by-step explanation:

Find out the equation of each line of the piece wise

First line

The first line has an open circle at (negative 2, negative 2) and it continues horizontally to an open circle (negative 5, negative 2)

(-2,-2) to (-5,-2)

$g(x)=-2$

$-5 < x < -2$

Second line

The second line has a closed circle at (negative 2, 0) and then continues up to an open circle at (1, 1.5)

[-2,0] to (1,1.5)

Find the slope

$m=(1.5-0)/(1+2)=0.5$

Equation in point slope form

$y-y1=m(x-x1)$

we have

$m=0.5$

$point (-2,0)$

substitute

$y-0=0.5(x+2)$

Convert to slope intercept form

$y=0.5x+1$

so

$g(x)=0.5x+1$

$-2 \leq x < 1$

Third line

The third line has a closed circle at (1, 4) and continues down to open circle (5, negative 4). Which functions represent a piece of the function?

[1,4] to (5,-4)

The equation of the line is

$g(x)=-2x+6$  ---> Repeat all steps that in second line

$1 \leq x < 5$

therefore

The piece wise function is equal to

$g(x)=-2$ ----> $-5 < x < -2$

$g(x)=0.5x+1$ ----> $-2 \leq x < 1$

$g(x)=-2x+6$  ---> $1 \leq x < 5$