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merlynthewhizz
Each inequality can be represented on a number line, as shown in the first picture below. 

Inequality of [tex]2\ \textless \ x \leq 3[/tex] is shown as a line from 2 to 3, the circle at 2 is coloured in white because the inequality sign is '<' whereas the circle at 3 is coloured in black because the inequality sign is '[tex] \leq [/tex]'. The values that meet the requirement of this inequality is all the value between 2 and 3 where 3 is inclusive.

The inequality [tex]3\ \textless \ x \leq 4[/tex] has white circle at 3 and black circle at 4 since the value for the inequality is between 3 and 4 where 4 is inclusive

The inequality [tex]1 \leq x \leq 2[/tex] has both black circle at the end since both 1 and 2 are inclusive

The inequality [tex]0\ \textless \ x \leq 1[/tex] has white circle at 0 and black circle at 1 since 1 is inclusive. 

These inequalities are represented on the graph as shown in the second diagram. The circles at 1 are joined since both are coloured black, showing both inequalities include 1.
Ver imagen merlynthewhizz

Answer:

2<x<=3  -------> f(x)= 3

0<x<=1   ------> f(x)= 1

1<=x<=2 ------> f(x)= x

3<x<=4 -------> f(x)= 4

Step-by-step explanation:

Range of the function

2<x<=3 , the graph is a horizontal line at y =3

So f(x)= 3

0<x<=1 , the graph is a horizontal line at y =1

So f(x)= 1

1<=x<=2 , the graph is a slanting line with slope = 1

we use equation y=mx+b , where m is the slope and b is the y intercept

There is no y intercept so b=0, slope =1 so m=1

So equation is f(x)= x

3<x<=4 , the graph is a horizontal line at y =4

So f(x)= 4

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