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$\text { Describe the indicated features of the given graphs.}$Follow the instructions of Exercise 35 for the function $y=x^{4}+c x^{2}$

Calculus 1 / AB

Chapter 24

Applications of the Derivative

Section 5

Using Derivatives in Curve Sketching

Derivatives

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In mathematics, precalculu…

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In mathematics, a function…

04:50

Graph the functions in Exe…

03:53

09:31

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05:53

06:49

05:08

05:54

01:09

Describe the graph of each…

we need the graph. The function given with this I would this equation. So the first thing we do is we determine what our parents function is. The parents function is why equals now, let me just look about the exchanges made to a to an equation When we exchange X in equation with X plus a positive number. This means that we are moving to the left. The graph is moving to the give the exchange use we X minus. A move is to the right. Well, we exchange why with what's left. It means that the graph will go down by a unit and will be exchanged. Why would I want a raise Positive number? It means that the graph go up. So the transformation, the transformation that we are witnessing here is X remains as it is. But why changes? Why has been replaced with Y plus four. Now, that's this situation here. So that means down down by four years. So how autograph? We grabbed the parent function by determining for six points on, then joining those points with her. Uh, this represents the third root off X squared. Done. A couple of these in previous excesses just to quickly select some exes, calculate the wise 011 for four. And now we performed transformation on these points for the new point on shift of grass are such that what happens toe? Why two weeks? Nothing. The X has remained the same. 01 minus 18 on a But the wise changed. They were down by four. Which means that each one is decreased about, for this becomes minus four. This becomes my three Martin three on four months for zero and Vera. So if you want to directly graph this function you could use these five points. You could add perhaps a couple of more points to make it more visible. Or you could graft the parent flexion, which I'm going to do with black. That line on the this would be a red solid line. I'll do it in this Muslim. Bring the breath over here. I'll be back in the second. Okay, we're back. Increase the area off the graph that's more visible you got. So I have included the actual increase into this more cells here. So why equals equals picks, which is X to the power of 2/3 that is dysfunction. Here. The points on that graph are 00 This one here 11 that we have 11 minus 11 is that one 84 is this point here. And minus 84 is the So with these three points for this wing off the parent faction on these three points for the other way, what was the transformation? The transformation waas down by four. So this one goes down by four 20 minus this one goes down by Put one minus three and so this point. Get down for here. This point moves them. This one on this point was found that one on that should be enough to he left information to breath the equation. So why plus four equals x 2 2/3 Is this regret? While the original breath waas pardon me? Apparent graph was X to the power to They're graphing by transformations. Hope it helps. All right,

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