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Juli2301 [7.4K]
3 years ago
8

A piecewise function g(x) is represented by the graph. On a coordinate plane, a piecewise function has 3 lines. The first line h

as 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
Mathematics
1 answer:
fenix001 [56]3 years ago
5 0

Answer:

see the explanation

Step-by-step explanation:

Find out the equation of each line of the piece wise

<em>First line</em>

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

<em>Second line</em>

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)

<u><em>Find the slope</em></u>

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

<u><em>Equation in point slope form</em></u>

y-y1=m(x-x1)

we have

m=0.5

point (-2,0)

substitute

y-0=0.5(x+2)

<u><em>Convert to slope intercept form</em></u>

y=0.5x+1

so

g(x)=0.5x+1

-2 \leq x < 1

<em>Third line</em>

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

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