In this lesson,
we will use the free online graphing
calculator linked below
to graph a function,
adjust the window,
then determine the intercepts.
The first step is to enter
the functions into the calculator.
And the calculator does
use function notation.
What the first function be F of X
and the second function be G of X.
Now let's go to the calculator
and enter the functions.
We need to clear the existing functions
and enter the new functions.
For F of X equals,
we enter 0.25 open parenthesis X minus
three, close parenthesis.
Raise the power of two
the caret exponent key is
Shift + 6 six and then we have minus five,
click in the cell for G of X,
G of X is equal to negative one, divided
by 10 X to the second power plus five.
And now I click Plot graphs.
Notice both graphs appear on the same
coordinate plane on the right.
But we do have to adjust the window,
in order to see the intercepts for both graphs.
We can zoom in and zoom out
using the plus or minus in the lower
right hand corner of the graph.
We can also reposition the graph left,
right, up or down,
using the arrows to the right.
Notice how if we click minus one, two,
three times with a very nice view of the graph.
Again, we can use the arrows
on the right to shift,
left, right, up, down.
We can also adjust the window manually
if we want, using the window option
in the upper left hand corner here.
And now let's go ahead
and to determine the intercepts
for the first function F of X,
which is graphed in blue.
If we have a hard time seeing the green graph,
we can change the color by
clicking on a color palette to the right
and selecting a different color.
For example, if we want the graph to be black,
we can click the black color,
click outside the palette and click plot graphs,
And now the graph is black.
Now let's work on determining
the horizontal intercepts for F of X,
which again, it's graphed in blue.
To do this, we click on the calculation
tab in the upper left.
Click on the select drop down menu
and we find the horizontal intercepts
by determining the routes or zeroes
of the function and therefore we click
the route slashes zero option,
notice now it says, "Click on the curve
you want to find the root of,
which is the blue graph."
Next we are asked to draw a box around the root,
So we draw a box around the x-intercepts,
but one at a time.
Let's first find the X-intercept on the left,
So we click, hold and drag a box
around the x-intercept.
When we let go, the horizontal intercept
is given as an ordered pair.
It's also given here in the lower
left in the calculation window.
We need to repeat the process,
to find the x-intercept or
horizontal intercept on the right.
We click the drop down menu, select route,
slash zero, click the curve
we're working with, which is the blue
parabola that opens up.
Draw a box around the route.
Notice how those two blues close together here,
But that's okay, because we already
selected the correct graph.
So we draw a box around the route or zero
and it gives us the approximate
coordinates of the x-intercept,
but is also shown here in the lower left.
And now to find the vertical
or y-intercept, which is this point here,
there's no calculation option for this
we need to recognize this is the Y value or
function value when the input
or X value is zero.
So to find the vertical or y-intercept,
we go down to the cell titled,
Type an expression and enter F of zero.
This will give us the Y value
or corresponding output
when the input are X value is zero.
The vertical intercept
is zero comma -2.75.
Let's go back to our work and record
the intercepts for the first function.
The horizontal or x-intercepts
are approximately -1.472
It will go round to three decimal places,
comma zero,
and approximately
7.472 comma zero,
And the vertical intercept
is ordered pair zero comma -2.75.
And now to repeat the process for our second
equation or second function G of X.
Since we already have the calculation tab open,
we click the mode,
select route zero,
Click on the Curve.
We want to find the route of
or x-intercepts of,
which is now the black graph G of X.
Draw a box around
the roots or x-intercepts.
Starting on the left, we draw a box around
the left x-intercept,
which gives us the approximate coordinates
of the first X or horizontal intercept
and repeat the process.
Under mode, select route,
Slash zero,
click on the black curve,
draw a box around the x-Intercept
or route on the right,
Click, hold and drag to draw the box.
Let go,
and we have the approximate x-intercept
or horizontal intercept on the right.
And again, notice how both are given here
in the calculation window.
And again, to find the vertical
or y-intercept, which is this point here.
We could see it's a zero comma five
because this is G of X,
We can find the vertical
intercept by entering G of zero.
Clicking Enter,
it will give us the output
of Y value of five.
Let's take this information
back to our slide and record the intercepts.
One of the x-intercepts for the second function
is approximately -7.071 comma zero.
Again, round to three decimal places
and the second x-intercept or horizontal
intercept is approximately 7.071 comma zero
and the vertical intercept
is order pair zero comma five.
I hope you found this helpful.