Sketching a graph under certain condtions

Question

I got a question like this,

sketch the graph of a function that satisfies the following conditions,

1. the domain is [0,oo];
2. the range is [4,oo];
3. the curve passes through [0,5];

while I was searching about domain and range I found this article http://www.analyzemath.com/Graphing/Graph_Abs_Val_Func.html

but I don't get it, I know how to pass the curve through [0,5] but what about domain and range?

I totally missed this lesson. Any examples please?

Answer 1

Usually we write infinite intervals as open at $\infty$, so the domain should be $[0,\infty)$ and the range $[4,\infty)$
The domain is the set of values you can take the function of. In this case it is the positive $x$ axis. So your function needs to have some value for all of that.
The range is the set of values your function can take. So there has to be at least one $x$ that results in $f(x)=y$ if I pick any $y \ge 4$
So I would start at $(0,5)$, drop down to $y=4$ then head off to the upper right corner of the paper.

Answer 2

What you want is a function that satisfies these criteria:

• f(x) for x<0 is undefined (this satisfies the domain, which is 0 to infinity)
• f(x)>=4 for x>=0 (this satisfies the range, which is 4 to infinity)
• f(0)=5 (this satisfies the point requirement)

So, first, draw a dot at 0,5, then sketch something to the right of that that dips down to y=4 and extends up/right indefinitely.