You can verify from
the picture that the three points I found are indeed on the graph.

You
will also need eventually to evaluate functions.

For the following
exercises, let .

Evaluate f(–3).

To evaluate a function,
I do just what I did above: I plug in the given value for x.
Here, I am supposed to evaluate at the value x
= –3. The notation
is different, but "f(–3)"
means exactly the same thing as "evaluate
at x
= –3"!

Note how I used parentheses.
It is very easy to mess up the minus signs if you're not careful and use
lots of parentheses. Take the time to be careful!

Advertisement

Evaluate f(3).

Evaluate f(–1).

Note that I gave the answer
in two formats: the "exact" form (with the radical in it) and
the "approximate" form (with the wiggly "equals").
Usually you will be expected to evaluate exactly; that is, it will usually
be correct to leave the answer in a messy form (with a radical, or a fraction,
or with pi
in it [instead of rounding to 3.14],
etc). However, there are times when the approximate form is better. Often,
word problems need an answer that can be applied in "real life".
For instance, "square root of 24
meters" isn't very useful when you're trying to figure out to what
length to cut a board, but "about 4.9
meters" is perfectly useful, and probably quite accurate enough for
whatever you're building. You will also need to approximate for when you're
graphing. For instance, I would have no idea where to plot the square
root of 24,
but I know right where to draw the line for
4.9.

By the way, you graph functions
just like you graph other equations: by evaluating the function at a few
values of x,
drawing the points, and connecting the dots. (This is exactly what a graphing
calculator does, by the way.) The graph of the function used in the three
examples above looks like this:

Just remember: "evaluate"
means "plug-n-chug". Be careful with the subtractions, negatives,
and exponents (by using parentheses appropriately). Don't try to do too
much at once; don't skip steps, don't try to do three steps at once, and
don't try to do everything in your head. Take your time, and evaluation
problems should work out fine!