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Problem 11 Easy Difficulty

Make a rough sketch of the graph of the function. Do not use a calculator. Just use the graphs given in Figures 3 and 13 and, if necessary, the transformations of Section 1.3.

$ y = 4^x - 1 $

Answer

We start with the graph of $y=4^{x}$ (Figure 3 ) and shift it 1 unit down to obtain the graph of $y=4^{x}-1$

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Video Transcript

Okay, So when making a refs catch of a function, we just kind of want to know if we know the basic shape of the function and the basic features. And if you want a rough sketch of Y equals four to the X power minus one, you should start with Y equals four to the X power. That's exponential growth, since the base is greater than one. So it looks roughly like this. Now what happens when we subtract one What we know from our experience with transformations that that should shift the graft down one. And the exponential growth function typically has ah, horizontal Assen towed at a height of zero. So who shift that down? One. It's going to have a horizontal asking towed at a height of negative. One soar graph is going to look something like this. If you want to get a little bit less rough, you could go ahead and plug in a couple numbers and plot a couple of specific points.