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PLS HELP ME

Graph the step function over the interval. -2 ≤ x ≤ 2.

f (x) = | x + 3 |

1 Answer

5 votes

Answer:

Certainly! Let's graph the step function

(

)

=

+

3

f(x)=∣x+3∣ over the interval

2

2

−2≤x≤2.

The absolute value function

+

3

∣x+3∣ can be broken down into two cases based on the sign of

+

3

x+3:

When

+

3

0

x+3≥0, i.e.,

3

x≥−3, the function is

(

)

=

+

3

f(x)=x+3.

When

+

3

<

0

x+3<0, i.e.,

<

3

x<−3, the function is

(

)

=

(

+

3

)

f(x)=−(x+3).

Let's consider each case within the given interval:

For

3

x≥−3:

(

)

=

+

3

f(x)=x+3

For

<

3

x<−3:

(

)

=

(

+

3

)

f(x)=−(x+3)

Now, let's plot these on the graph:

For

3

x≥−3:

Draw the line

=

+

3

y=x+3 over the interval

2

2

−2≤x≤2.

This line starts at

(

3

,

0

)

(−3,0) and goes upwards with a slope of 1.

For

<

3

x<−3:

Draw the line

=

(

+

3

)

y=−(x+3) over the interval

2

2

−2≤x≤2.

This line starts at

(

5

,

0

)

(−5,0) and goes downwards with a slope of -1.

The graph will consist of two line segments. I recommend using graph paper or a graphing tool for a more accurate representation.

Explanation:

User Halona
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