Question

What is the graph of this function?

Answer 1

We are given a function,

`y=(|x|+2)/(2)` if 0 ≤ x < 6

We need to draw the graph of the function.

We know that Parent function of the given function is Modulus function | x |.

Consider given function,

`y=(|x|+2)/(2)`

`y=(|x|)/(2)+(2)/(2)`

`y=(|x|)/(2)+1`

So, the given function is translated 1 unit upward and compressed by factor of 1/2.

So the obtained graph is attached.

Answer 2

See attachment.

Explanation:

The main part of the function is an absolute value function and so it forms a V with the center of the V at (0,0). The sides of the V go up and over 1 unit at a time. However, since 2 is added to the it outside of the absolute value, the center of the V moves from (0,0) to (0,2). The sides stay the same. The division by 2 changes the sides. The sides move from up and over 1 unit to up 1 unit and over two units. It spreads or widens the graph. Lastly, the interval selects a specific part of the graph only from 0 to 6 on the x-axis. This takes just one side of the V and looks like a line segment. See attachment.