In Exercises 1–4, the graph of an exponential function is given. ...

Question

In Exercises 1–4, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4^x, g(x) = 4^-x, h(x) = -4^(-x), r(x) = -4^(-x)+3 1.

Accepted Answer

Hello. Everyone in this video. We're going to be looking at this graph and we're going to try to find an equation that fits with the graph the best. And you can see that we're going to be working with exponential functions. So recall that an exponential function let's say for example to to the X. We'll have this sort of U shape where increases as it goes to the right and it starts off at zero. So it has a a cento at Y equals zero normally. And that's when we have just two to the X. Um Our graph seems to be translated in the why access. So if I flipped this black line over in the y axis it would have more this shape and that's exactly the shape that we're seeing in this graph. So that means that we have two to the negative X. Present. So I can eliminate any answer choice that has a positive exponent and you can see that B has this positive X. So I can eliminate B. However, if you didn't recall what the basic what the shape is of exponential functions or what the translation means, we can also use this 0.0 to to solve or to check each one of these equations. So I'm going to go ahead and do that. So a saying f of X is equal to two to the negative X. So f of X is equal to Y. So I have two is equal to 2 to the zero. Anything to the zero power is one. So I have two is equal to one and I know that's wrong. So that would eliminate A. If I look at B I have negative two x -2 to the X minus one. If I plug in sorry let me rewrite this. I have g. of X is equal to -2 to the X -1. G of X is equal to Y. Which is two. That's equal to negative two to the zero minus one. So now I have two is equal to zero Or 2 to the zero is 1 -1. Talisman two is equal to zero and that means that B is not viable answer which we had already interpreted that if we look at sea I have H of X is equal to two to the negative X plus one. H of X is equal to Y. So two is equal to two to the negative zero plus one which means two is equal to one plus one. So two is equal to two. And that is true. So C could be an option. Let's make sure that D it's not an option. So D. Is our Of X is equal to negative two to the negative x. R, F X is y. So I have two is equal to negative two to the negative zero, which means two is equal to one and that is not true. So thankfully C is the only one that worked out which means that C is our answer. So it can be easy to remember the sort of visualizations of the exponential functions. But if it's too much memorization, you can always just plug in the point that they give to check it. So hopefully this video helped and see you next time.

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

In Exercises 1–4, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4^x, g(x) = 4^-x, h(x) = -4^(-x), r(x) = -4^(-x)+3 1.