Today we’re going to talk about how to find coordinate points and the domain and range
of a function just by looking at the graph of a function. To complete this problem, we’ll
look for points on the y axis that correspond with points on the x axis then, to find domain
and range, we’ll look for all x and y values that the function attains.
Let’s take a look. And in this particular problem, we’ve been
asked to find f of one and f of five, as well as the domain and range, based on the graph
of the function. So, the first part of finding f of one of
five is just interpreting values from the graph. When we’re asked to find f of one
and f of five, all we’ll be doing is looking at the y value for the function when x is
equal to one and five. So, for example, f of one, we can locate the point on the x axis
where x equals one, so that’s this point right here, and to find the corresponding
y value, we just go up and meet the graph wherever it is and we see that we get to the
graph of this point, if we go over to the left, we see that we have the y axis at three
right here so we know that f of one is equal to three, and this basically means that we
have the coordinate point (one, three), where x is one and y is three, on the graph of our
function. So, same thing here with f of five, we find the point along the x axis where x
is equal to five and we go down in this case to meet our function. So, we come down here
to meet our function and if we come back over to the y axis, we see that we run into approximately
negative two. I haven’t drawn this graph perfectly but the idea is we run into negative
two here on the y axis so we get negative two for f of five. And, that tells us that
we have a coordinate point on our… on the graph of our function of (five, negative two).
That means that when we plug in five to our function, we’ll get back a value of negative
two, or when we plug in one to our function, we’ll get back a value of three.
So now, when we talk about domain and range, we wanted to find that domain is all of the
x values for which the function is defined. So we just need to give a list or a range
of all x values that this function could possibly attain. And if we look at the graph of this
function here, we can see that the smallest x value it attains is x equals zero, right.
There are no x values to the left of this point for which the function is defined. This
is where the function starts on the left hand side; it ends here on the right hand side.
So we know that the domain runs from this point all the way to this point and the left
hand side here is equal to zero, the right hand side is equal to seven. So we can say
that the domain is x greater than or equal to zero and less than or equal to seven. We
can also write that as in square brackets like this, [zero, seven].
Now, the range is the corresponding set of y values that the function can attain based
on the domain that we’ve already defined. So, on this… on this domain here from zero
to seven, which y values can the function attain? Well, we can see here that… (we’ll
use a different color) we can see here that the highest y value is at this point here
and that the lowest y value is at this point here so we know that our range runs from this
point to this point, that’s the range. The y coordinate at the top of our range here
is four and at the bottom, it’s negative two, so we can say that the range is y greater
than or equal negative two and less than or equal to four, and, again, we can write that
as negative two to four. And that’s all there is to it. That’s
how you can find coordinate points or values from your function, and domain and range from
your function, just by looking at the graph of the function even when you don’t have
the function’s equation. So, I hope you found this video helpful. If
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