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Go to https: WWW. desmos.COI , and graph the function f(x) =e-V/r_ This function can be entered as exp(34) Note that the domain of this function is all real v excep...

Question

Go to https: WWW. desmos.COI , and graph the function f(x) =e-V/r_ This function can be entered as exp(34) Note that the domain of this function is all real v except 0, and it has no € - y-intercepts_ The graph should show several other notable features , which you will now explore points each)

Go to https: WWW. desmos.COI , and graph the function f(x) =e-V/r_ This function can be entered as exp (34) Note that the domain of this function is all real v except 0, and it has no € - y-intercepts_ The graph should show several other notable features , which you will now explore points each)



Answers

Use a computer to graph the function using various domains and viewpoints. Get a printout that gives a good view of the "peaks and valleys". Would you say the function has a maximum value? Can you identify any points on the graph that you might consider to be "local maximum points"? What about "local minimum points"?

$ f(x, y) = 3x - x^4 - 4y^2 - 10xy $

This is the equation were given. And if we zoom in a little closer, we can see some important values on the graph being relative maximum on routes of minima as well as the, um, why intercept on none of the X intercepts? But if we showed like this, we're able to see all that we need to with the graph because the domain ist or in numbers.

So the first thing we wanna do is graphically given function. So around right at the given function F. Of X equals 1/4 cubed plus three. Keep in mind that we're wanting to plot points so we can pick corresponding exercise and get their resulting Y values. So for example if we plug in a zero we'll get three. If we plug in a negative uh Two. Okay. A negative too. And if you plug in a positive too greater positive five, there should be a negative two plus three. So one. Um And then one more point. I will plug in say um A four and get 19. And then we'll plug in a negative four. You got fixing? Alright negative 16 or maybe a 13? That'll be this is what we end up getting. As a result graph looks like this. So we see that the domain and range are both all real numbers.

We're going to be using the graphs of F and G. I have to answer some of the questions. So we want to identify the domains and ranges. So let's just look at a general function F of X equals X cubed minus two X. So domain we want to remember is the set of all X values such that F of X is defined. It's a defined number. So we see in this case that the domain is all real numbers because we can plug in any value of X and get a defined output value fx. Now, if we look at some other functions such as the square root of X, we see that the domain is from all values zero or less greater than or equal to zero. Because if we plug in any value less than zero, we see that would be undefined. It would be an imaginary number. So that's how we identify domain. And then range is going to be all values similar to the domain, but the range is going to talk about the Y values. So any why value that we can end up getting in our function. So here it will be from zero to infinity. Before if we have like X cubed, it will be from negative infinity to positive infinity.

Just consider the giving function that is FFX is given to us as two raised to the X -4. So now we're here we just have to grab this giving function and also we just have to do to mind the domain as well as the rage. So now we're here and just going to draw the craft of just giving function F. Of X equal to two raised to the X minus four from the parent graph. Where you can see from the base graph of G. Of X equal to to rest to deeper X. We are already familiar with the graph of uh G X equal to to rest to deeper X. So as you can see this blue dashed girl over here, this represents the graph of G of X equipped to to raise two people X. Now the function, the graph of the function F of X will be obtained from the graph of G of X by translating it four units downward. As you can see it is minus four over hill. That means you will just translate the graph of G of X four units downward. Okay, so when you just do that, as you can see here on the graph on the left hand side, on translating the graph of G of X four in its downward, we'll get this green cove over hill that represents a graph of to raise to the bar X minus four. Now, as I said, we're also supposed to determine the domain and the range. So domain is simply is the state of all the X values that the function way. So as you can see over here, the graph is ranging from minus infinity to infinity. And talking about the range, as I say, that is simply the set of five values. And therefore from the graph you can see that the ranges from minus photo infinite.


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