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 3.

Accepted Answer

Hello. Everyone in this video. We're going to be looking at this graph and we want to determine which function is being represented in the graph. So from the answer choices you can see that we're dealing with from the answer choices and the prompt you can see that we're dealing with exponential functions. And in this case it seems like we're going to be working with three to the X. Whether that X is negative or positive. And just by looking at the graph shape we can tell that the three is going to be to the power of a negative exponent. Because if it was to the power of a positive exponent it would follow this shape going upwards but instead it is being reflected across the sort of Y axis to form this shape. So knowing that I can eliminate all the answer choices that have positive exponents on the three. Which means that D. Is not a good function for me. Now we can go ahead and look at the other options. Notice how the last three options for the next three options all have negative three to the negative X. And the only difference is they have this - Or this plus two or nothing. So recall that the -2 or the plus two outside of the exponent correlate to a vertical translation. Which means that we're gonna be shifting the graph up or down. So recall that normally our ascent tote is at X equals zero. Meaning that this graph. If it followed the same shape it would normally approach Why Equal zero. Sorry? However this one doesn't approach why equals zero. It approaches y equals two As it goes to infinity and I say approaches why equals two. Because you can see that this line Gets really close to y equals two, which is this dotted line as it continues. So that's where we have innocent. So our ascent shifted upwards by two units, which means that we have to consider a vertical translation. So because there is a translation, we can eliminate option B, which has no translation. And now we need to remember Which of the two options it is so we have -2 or plus two. And in this case we shifted upwards by two. So we actually want the plus two and this minus would be shifting it down two. Y is equal to -2. And this plus is shifting it Up to Y is equal to positive two. So answer choice C. Is the equation that most that is being represented in the graph. So hopefully this video helped and see you next time

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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 3.