In this video,
we will graph the given
log function on the TI-84,
as well as give the domain
and range and the equation
of the vertical asymptote.
Because y equals negative
log base three of x,
and the graphing calculator
only contains common log
or log base 10, as well as a
natural logarithm log base e,
we will have to use the change
of base formula shown here below
to graph this function on the TI-84.
We can either use common
log or natural log.
In this example, let's use common log.
Y equals negative log base three
of x is equal to negative common log
of x divided by the common log of three.
Now, before we graph this,
we should be able to recognize,
because we just have
log base three of x here
where the input is just x,
the domain is going to
be x greater than zero,
or the open interval
from zero to infinity,
and the vertical asymptote is
going to be the line x equals zero,
and this negative sign here is not
going to change the range,
the range is still all real numbers,
or the open interval from
negative infinity to positive infinity.
Let's go ahead and record this
but we will also check it graphically.
Going to the calculator,
we press y equals and then enter negative,
not minus but negative common
log x close parenthesis
divided by common log three
close parenthesis and enter.
And now to make sure we
have the standard window,
let's press zoom six.
Zoom six gives us z standard
or the standard window.
So now that we have a decent
graph of the function,
we could adjust the window,
but from here we should be able to tell
that the vertical
asymptote is x equals zero,
the domain is the open
interval from zero to infinity,
and because the the graph does go down
as well as up indefinitely
without any holes or breaks,
the range is the open interval
from negative infinity
to positive infinity.
But now to make our graph,
we want to find some
convenient points on the graph,
and there's two ways of doing this.
One way is to press zoom
and then four for z decimal,
which actually gives us a better window,
but now if we press trace and
we scroll along the function,
notice how the x values
increase by 1/10 so notice how
if we keep scrolling, we can
see the point one comma zero
is one point on the graph of the function.
Let's scroll out to x equals three.
Notice how the point
three comma negative one
is also a point on the function.
Our coordinate plane
only goes out to eight,
so let's determine the
y value when x is six.
Notice how when x is six,
we would have to approximate
the function value
which is approximately negative 1.63.
Another way to find a point
on the graph would be to use the table.
Let's also show this method.
Let's first press second
window for the table set.
Right now the table's
going to start out at 5.5.
Let's start the table at zero, enter.
The change in the table
is by .5, which is fine.
We want both independent
and dependent variables to be
on automatic which they are.
So now if we press second graph,
we can scroll down the table
and find convenient points.
So again, here we have one comma zero,
three comma negative one,
and let's also use six comma
approximately negative 1.63.
Let's begin by sketching
the vertical asymptote
of x equals zero, which is the y-axis.
One comma zero is the horizontal
intercept or the x intercept.
And we have three comma negative one,
and then six comma negative 1.63,
which is approximately here.
We know as x approaches zero,
the graph is going to approach
the vertical asymptote
where function values approach infinity,
and therefore on the left,
the graph looks something like this.
And then to the right, the
function continues to decrease,
and looks something like this.
I hope you found this helpful.
