Need help on these Functions ASAP! Thank you!

Question

A step function is shown below.

1. Complete the table below.

x	f(x)
0
0.5
1
1.5
2
2.5
3
3.5
4

1. Using the table above, you may notice some type of a rounding pattern. What is the pattern?
2. Create a piecewise function notation for the graph above, over the interval -4 ≤ x ≤ 4.

Answer 1

≤1.      Complete the table below

x	f(x)
0	1
0.5	1
1	1
1.5	1
2	3
2.5	3
3	3
3.5	3
4	5

2.      Using the table above, you may notice some type of a rounding pattern. What is the pattern?

Using INT(x) as the function that returns only the integer part of the result:

    f(x) = 2*INT(x/2) + 1

3. Create a piecewise function notation for the graph above, over the interval -4 ≤ x ≤ 4.

The piecewise function is:

    f(x) = { -3 for -4 ≤ x < -2

                    -1 for -2 ≤ x < 0

                     1 for 0 ≤ x < 2

                     3 for 2 ≤ x < 4

                     5 for 4 = x

     If you can write f(x) using INT(x), then:

         f(x) = { (2*(INT(x/2) + 1 )  for -4 ≤ x ≤ 4

Answer 2

Hey Logan! So the first thing you need to pay attention to for this piece-wise function is where the line, or function, is solid versus where there’s a hole. A function can only have one y-value at any given x. At x = 0, there is a hole at y = -1, meaning there is no value there. However, there is a solid point at y = 1. Therefore, at f(x)=f(0), or when x=0, y is 1. At f(0.5), there is still a solid line at y=1, thus f(0.5)=1. Make sense?

Visually, find each value of x they ask for, and draw a line vertically up and down. Wherever that line hits the function at a solid point, that’s the value. This is called the vertical line test. The answer to your problem is as follows:

f(0)= 1

f(0.5)=1

f(1)=1

f(1.5)=1

f(2)=3

f(2.5)=3

f(3)=3

f(3.5)=3

f(4)=5

Hope this helps.