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Hi everyone! 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 you did, like this video down below and subscribe
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