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Ax+b Describe how the graph of f (x) can be obtained from the graph of cx+d (x) Make sure vou describe the transformation(s) in terms of 0, b, and/or d. Show all wo...

Question

Ax+b Describe how the graph of f (x) can be obtained from the graph of cx+d (x) Make sure vou describe the transformation(s) in terms of 0, b, and/or d. Show all work on this sheet:

ax+b Describe how the graph of f (x) can be obtained from the graph of cx+d (x) Make sure vou describe the transformation(s) in terms of 0, b, and/or d. Show all work on this sheet:



Answers

Describing Transformations Suppose the graph of $f$ is given. Describe how the graph of each function can be obtained from the graph of $f .$ $$ \begin{array}{lll}{\text { (a) } f(x)-1} & {\text { (b) } f(x-2)} & {}\end{array} $$

All right, So we're gonna assume that we're starting out with the equation and the graph of why equals f of X, Then we're gonna look at the transformations. So for part, they were given and a negative X. So what would be the transformation from this ground to describe? So we see that there's a negative sign since it's on the inside of the parentheses with the X, we know that this means it will be reflected about the why access and then on part B, given three f of x. So from why equals of of ex craft to this graph, there's a three constant out in front of the equation. So when there's a constant either stretches or shrinks the graph. So since this is a three outside of the equation F of X, that means that it's gonna vertically. Since it's on the outside, it vertically stretches it by factor of three

Okay. Hello, everyone. So today we're dealing with transformations of black, so pay. So suppose your original graph is ever backs equals expert. So it's operable. Restaurant floor. So what happens if we multiply Negative one to apple backs? Ok, not to act to apple backs entirely. So, yes, you can see here for every X value se for it. This one right here. Negative 1.42 down here. Negative one point for you to Yeah, approximately. The y coordinate is also multiplied by negative one. Right. So in this case, we call the special nation a reflection about the X answers. Okay, but what about when we're multiplying the entire function again? Not just X by 1/3. So this time, for every X value, the corresponding why value is multiplied by 1/3. Okay, so this is why so, for example, again, if I pick a random point, say Yeah, one point even of 1.4, we have 1.96 because what? Because our y coordinate right. So very similar. Goodbye. Pick around here. Negative one point Warren, right? Yeah. That's what I said you could have one going for around here. So the white corn is actually divided by three. Pray. How fascinating is it? I know. Yeah. So in this case, this is a Skilling so not a shifting The graph has not moved upwards or downwards. But rather it is in this case, What does it look like? So it's actually stretch right by a factor of 1/3. Yeah, and that's it. Thank you so much for listening on. Have a great day.

Hello, everyone. So we'll be talking about transformations of graphs today, So suppose that our original function is above X equals X squared. Okay, So what happens if I add five to acts? Okay, only two x not to have a fax. Right. What happens? So if you add or subtract something from axe directly, that is gonna be a horizontal translation, right? Because so, X access. Horizontal translation. It's very simple, but keep in mind that horizontal translations are always inverse. So when we adding five to act, you are actually moving your graph you left by five units. Okay, so why so a very example Be very simple example. Is that so? The original point of the original function, the purple one as 00 Right. And now the new point. This negative 50 So for horizontal translation, why doesn't change why I slept alone but acts changers So think about like this. The graph has to compensate for that change, right? By moving itself to the left five units so that it still has the same y coordinate right, because his euro square equals your own. But zero plus five square equals by square or 25. So X has to be negative five. So that negative five plus five equals zero. Where also zero. Okay, so that is horizontal translation. Political translation is when we're adding, afford directly, you apple box. So the key thing here to keep in mind is that weather that four is grouped with X or whatever backs. And in this case, plus four is worked Would happen. Facts right and radical. Translation. It's very straightforward when you're adding for it to your graph your grammar. Simply moving upwards by four units. Okay, So original 0.0 new point is now zero for right, So zero square equals zero, but zero plus four equals four. So that's why I'm new. Grab this work upwards by four units. Okay, So it can remember if X is grouped with that component, and that would be horizontal translation. So if it adding or subtracting horizontal translation. But if the component is at it, is that a tour subtracted from Activex? That is going to be a vertical translation. Okay, So shifting downwards or upwards. OK, so thank you. So looking listening. You really about this house

All right, so we're given to equations with Port A. Our first equation is ever vax equals X squared. Our second equation is G of X equals X plus two squared. And what we're looking for is explaining how we get this graph this equation from this graph of this equation. So we know that we can see that there's a transformation here. So there's a constant plus two on the inside of the G of X function. We know that's wrong when it's on the inside. That means that it is shifted either from going to the left or going to the right in this case, and that's positive. You get the graph g of X by shifting to the left. Two units right then for Part B were given after Max equals X squared GM X equals X squared. No parentheses, plus two. So in this case, our transformation is plus two and there's no parentheses, so we know that either shifting up or down, since it's positive you get g of X from f of X by shifting the graph up two units


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