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Current time:0:00Total duration:3:15

CCSS.Math: ,

- [Voiceover] We're told, use
the interactive graph below to sketch a graph of y
is equal to negative two, times three to the x, plus five. And so this is clearly
an exponential function right over here. Let's think about the behavior as x is, when x is very negative, or when x is very positive. When x is very negative, three
to a very negative number like let's say you had three
to the negative 3rd power, that would be 1/27th, or three
to the negative 4th power, that would be 1/81st. So this is going to get smaller,
and smaller, and smaller. It's going to approach zero
as x becomes more negative. And since this is approaching zero, this whole thing right over
here is going to approach zero. And so this whole expression is, if this first part is approaching zero, then this whole expression
is going to approach five. So we're going to have
a horizontal asymptote that we're going to approach
as we go to the left. As x gets more and more negative, we're going to approach positive five. And then as x gets larger,
and larger, and larger, three to the x is growing exponentially. But then we're multiplying
it times negative two, so it's going to become more,
and more, and more negative. And then we add a five. And so what we have here,
well this looks like a line. We want to graph an exponential. So let's go pick the
exponential in terms of x. There you have it. And so we can move three things. We can move this point,
it doesn't even need to just be the y-intercept, although that's a convenient
thing to figure it out. We can move this point here. And we can move the asymptote. And maybe the asymptote's
the first interesting thing. We said as x becomes
more, and more, and more, and more negative, y is
going to approach five. So let me put this up here. So that's our asymptote. It doesn't look like it quite yet, but when we try out some values for x and the corresponding y's, and we move these points accordingly, hopefully our exponential
is going to look right. So let's think about, let's
pick some convenient x's. So let's think about
when x is equal to zero. If x is equal to zero, three
to the zeroth power is one. Negative two times one is negative two, plus three is three. So when x is equal to zero, y is three. And let's think about
when x is equal to one, and I'm just picking that
'cause it's easy to compute. Three to the first power is
three, times negative two is negative six, plus
five is negative one. So when x is one, y is negative one. And so let's see, does
this, is this consistent with what we just described? When x is very negative,
we should be approaching, we should be approaching positive five, and that looks like the case. As we move to the left, we're
getting closer, and closer, and closer to five, in fact,
it looks like they overlap, but it's really, we're
just getting closer, and closer, and closer 'cause this term, this term right over
here is getting smaller, and smaller, and smaller
as x becomes more, and more, and more negative. But then as x becomes
more and more positive, this term becomes really negative 'cause we're multiplying
it times a negative two, and we see that it
becomes really negative, so I feel pretty good about
what we've just graphed. We've graphed the horizontal
asymptote, it makes sense, and we've picked two
points that sit on this, on the graph of this exponential. So I can check my answer,
and we got it right.