Question 205 ptsYouare given graphs of 3 different functions, with each function having an equation of the form 3 = 8(6)".Which graph has the larget value for ...

Write the function whose graph is the graph of $y=x^{3},$ but is: Vertically stretched by a factor of 5

Okay, so we're asked to find either a minimum or maximum. That depends on whether a is positive or negative. And we can see here. Yes, it's a fraction, but it is positive. So that means that this is gonna open up and so we're gonna have a minimum. And so we find that by using first the, uh X value to find out where access of cemetery is, And then that will tell us once we find out why I value what are minimum is. And so first I start with the negative. Be over two A. And so here I use a negative to over two times a day, and a is 1/3 so we can see these twos. Cancel And remember, when I'm dividing by a fraction, I just multiply that negative one That's left times the reciprocal of this fraction. So that's times three over one or times three. And so that's a negative three. So that I'm gonna plug this negative three back into this equation and find why. So what I get is a 1/3 time's oops times negative three squared, plus two times a negative three plus five. And so we first do the exponents cause that's the correct order of operations. And we are going to square a negative three, which is just a positive nine. So this becomes nine and then nine, divided by three is going to be three. Plus. Let's actually go back here because the negative three times a two is a negative 60 well, this will be minus six and then plus five. And so we've got here is three minus six where you can combine the positive. So I have a five and a three, which is eight. So eight minus six gives me too. So my minimum is at, too. And you can say also that the point is negative three common to but again or minimum is related to the why value. And so that's what they were asking us for.

Equals toe X Q minus like for excess with two and minus two. So we should make table here. Four x and y. Let's say this is sex and California value of why we're trying to find seven Xs minus off to why we have minus eight minus minus, starting minus three The wide way, too. We have the value off White, which is minus three. Divide way toe that is 1.5 raised with paltry like this *** deal of 8.2. When it is *** Table one, we have bigger deals. Six. When it is a bigger deal, one divide way, too. We have 5.12 where the little we have bigger deal fight When it is one, we have one Divide by two. We have 0.5 days to Port ST minus like is a bigger deal. 4.87 It is one. We have one minus five with dignity off when it is a three d white way, too. We have 1.5 station, about three minus. Life is bigger. People 1.5 days aboard, three minus five is getting off 1.625 although when it is too. We have eight minus five in ST. Well, we should mark x and y access. So 123 You it iss x And why? So look, save your saying that 0.8 Beat C D E f. The trend two point is minus two minus 13 minus two minus what it is too little. Minus two minus one minus two minus three minus minus five minute states minus seven. Minus eight. Minus night minus 10. Minus 11 minus two A minus 13. Here. So we have this point is a the point to be We have minus C Y tu minus 8.375 Be at this point. It's be why in C minus one minus six This point, Wendy's little minus. Why indeed? De is north zero minus point. De is negative off one by two. And here it is. ***, table 5.1. Do so you know, even this point be and we have this point. It is E. Now, if we have one way to negative 4.875 school this point we have for see, we have one negative four and see. Poor wretch. We have three very well, toe negative 1.625 That IHS, Some of you, we do that. And it is to this three *** deal fight and it is negative. Oak Street Soul three D Mind my to raise to bar three toe. So just plus three at two were getting blustery. So look to someone here it is. +123 When we're joining these points, it's very quiet about which is why x cubed minus five.

So 86 were given at the backs. He grows 3/5 that square. I they want us to do the Vertex of by minus six. So this is your ex decision. Why That order, remember, is X equals 3/5 so it's X minus five square minus.

Okay, so in this problem, we're looking at the function five to the ex. So we need to find three ordered pairs. That's really simple. Just plug in numbers. So fire to the zero power. Anything to zero power. That's one five to the one. So whenever X is one, we just saw five and then fire to the two that's gonna get me five squirt. We're just 25. So look, I got three points already. Only have to do is stick in a number for X. And And so then I could sketch a graph, but I'm just gonna use decimals. So then let's see. Four points are there. We got zero to the one, and then we got one to the five. Yeah, and then two to the 25. So are on there. Yeah, I was only five. Okay, Noah State, the dominant range who don't mate her domain ISS. You can't find a starting point, so it's negative affinity, and then you go to the rights and it still goes on forever. So it's all real numbers. That's it for this. Okay. Ah. Okay. So then domain is all real numbers and then range, Range you start from the bottom to the top, so see range ISS, but on the bottom, there's nothing there until you hit the zero. It's because zero is your horizontal assets. Hope so. A NASA don't means you have a graph. It'll get really close but will never touch it. So it'll get closer to zero but never touch it. See you do an open bracket. 02 infinity and I will be strong, He arranges zero thio infinity because it goes up forever. Or you can say why is greater than zero? Because while your wife values are bigger than the number zero, it's never gonna equal to zero okay and its function as you go from left to right, the numbers keep getting bigger. It's growing. It's getting farther from the acid tope. So it is increasing, so don't mean it's all remembered. Range is why is greater than zero, and the function is increasing