Question

Match the portions of piecewise functions represented in the graph with their corresponding ranges of x-values.

Tiles
f(x) = 1
f(x) = 5 − x
f(x) = 2
f(x) = 3
f(x) = x
f(x) = 3 − x
Pairs
Range of x-values Portion of Piecewise Function
2 < x < 3=
0 ≤ x < 2=
3 < x ≤ 5=
x = 2 =

Answer 1

From left to right
1) f(x)=x, range 0 ≤ x < 2
2)f(x)=3 , range x=2
3) f(x)=1, range 2 < x < 3
4) f(x) = 5 − x, range 3 < x ≤ 5

Answer 2

Answer: f(x) = 1 ; 2 < x < 3.

f(x) = 5 − x ; 3 < x ≤ 5.

f(x)= 3 ; x=2

f(x) = x; 0 ≤ x < 2.

Explanation:

For the graph for line y=1, we have x range from 2 to 3.

Therefore, f(x) = 1 ; 2 < x < 3

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f(x) = 5 − x

For the line segment y=5-x, we have starting x value is 3 and last value of 5.

Therefore, f(x) = 5 − x ; 3 < x ≤ 5.

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f(x) = 2

f(x) =2 don't fall any x value, because we have hollow dots on y=2.

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f(x) = 3

F(x) =3 fall when x=2.

Therefore, f(x)= 3 ; x=2.

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f(x) = x

For the line segment y=x, we have starting x value is 0 and last value of 2.

Therefore, f(x) = x; 0 ≤ x < 2.

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f(x) = 3 − x

f(x) =3-x don't fall any x value, because we don't have any segment y=3-x there.