Sketch a graph of y=2^x and carefully draw three secant lines ...

Question

Sketch a graph of y=2^x and carefully draw three secant lines connecting the points P(0, 1) and Q(x,2^x), for x=−3,−2, and −1.

Accepted Answer

Welcome back, everyone. In this problem, we want to draw the graph of Y equals 3 to the power of X and include two C lines that connect the point P 13 to the point Q X 3 X X equals -2 and the -1. Here we have a grid on which we'll draw our graph. Now, what do we know here? First, let's start by putting the point P on our graph and P is at 13. So it would be at this point, OK? So this is the point P. Now, notice that we're joined the graph of Y equals 3 X. And when X equals 1, OK, then Y would be equal to 3 of 1 which equals 3, which means that the 0.13 is on our graph, OK? So P is on our graph. Next, when X equals -2, OK. Notice here. That Y is going to be equal to 3 the power of -2. That's 1 divided by 3 squared, which is 19th. So that tells us negative 2 1/9 is also on the graph of Y, OK? Which makes sense because here if you compare it to the point Q, notice that that's how we would find it when X equals 2, OK. So when X equals 2, we know that Q would be, sorry, when X is -2, Q would be 2 and 3 to the power of -2, which would still give us -2 19, OK? So if we put -219, it would be somewhere down here, OK. So that point I know when X equals -1. X equals -1, then Y will be equal to 3-1, which equals 1/3. So 1 1/3 is on Y. Now, when we draw that, it would be right here, OK? Know that we have these points, we can use them to plot the graph of Y. Plot the exponential function Y equals 3 of X. So when we connect these lines, OK, we should probably try it here. Let me probably put it in blue. Then our curve would probably look something like this, OK. So this would be the graph of Y equals 3 to the power of X. Now, we also know that these two points that we found earlier are the points through which our Cant lines will pass, OK? So now, we're going to, for, for the point where X equals -2, we're going to draw a C line, OK. From negative to 19 to 13, OK. And that C line is probably going to look something like that. And then in red, we'll draw the other one where X equals -1 up to the point P and that graph would probably look something like this, OK. So now, here's the graph of Y equals 3 to the pore of X and the two C lines passing through -219 and 13 and -113 and 13. Thanks a lot for watching everyone. I hope this video helped.

Sketch a graph of y=2^x and carefully draw three secant lines connecting the points P(0, 1) and Q(x,2^x), for x=−3,−2, and −1.

Key Concepts

Exponential Functions

Secant Lines

Graphing Techniques

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