The point of this section is to introduce you to some other
functions that don’t really require the work to graph that the ones that we’ve
looked at to this point in this chapter.
For most of these all that we’ll need to do is evaluate the function as
some x’s and then plot the points.
Constant Function
This is probably the easiest function that we’ll ever graph
and yet it is one of the functions that tend to cause problems for students.
The most general form for the constant function is,
where c is some
number.
Let’s take a look at so we can see what the graph of constant
functions look like. Probably the
biggest problem students have with these functions is that there are no x’s on the right side to plug into for
evaluation. However, all that means is
that there is no substitution to do. In
other words, no matter what x we plug
into the function we will always get a value of 4 (or c in the general case) out of the function.
So, every point has a y
coordinate of 4. This is exactly what
defines a horizontal line. In fact, if
we recall that is nothing more than a fancy way of writing y we can rewrite the function as,
And this is exactly
the equation of a horizontal line.
Here is the graph of this function.
Square Root
Next we want to take a look at . First, note that since we don’t want to get
complex numbers out of a function evaluation we have to restrict the values of x that we can plug in. We can only plug in value of x in the range . This means that our graph will only exist in
this range as well.
To get the graph we’ll just plug in some values of x and then plot the points.
The graph is then,
Absolute Value
We’ve dealt with this function several times already. It’s now time to graph it. First, let’s remind ourselves of the
definition of the absolute value function.
This is a piecewise function and we’ve seen how to graph
these already. All that we need to do is
get some points in both ranges and plot them.
Here are some function evaluations.
x

f(x)

0

0

1

1

1

1

2

2

2

2

Here is the graph of this function.
So, this is a “V” shaped graph.
Cubic Function
We’re not actually going to look at a general cubic
polynomial here. We’ll do some of those
in the next chapter. Here we are only
going to look at . There really isn’t much to do here other than
just plugging in some points and plotting.
x

f(x)

0

0

1

1

1

1

2

8

2

8

Here is the graph of this function.
We will need some of these in the next section so make sure
that you can identify these when you see them and can sketch their graphs
fairly quickly.