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2 +52 35_ What is the range of the function g(x)...

Question

2 +52 35_ What is the range of the function g(x)

2 +52 3 5_ What is the range of the function g(x)



Answers

Find the range of each function when the domain is $\{-3,-1,0,1.5,4\}$.
$$
y=-(x-5)
$$

So for the given function five course of two T. The range is maximum value to minimum value evidence and minimum to maximum. So minimum will be fancy. Net minus by which will be five off fourth of minus pi. Which will be -5 and f off. Mhm. Zero. We'll give the maximums of five costs of zero will be five. So this range will be Here minor equals two -5-5 and the graph can be plotted. As shown Graph will start from five and It will reach 2 -5 then again at five. So this is that.

We need to find the range of the given function and then we need to determine the values of X. That make the function equal to two. So the number in front of X squared is A. The number in front of X's B. And then we have C. So if A. Is positive, our graph opens up and we have a minimum if A is negative, our graph opens down and we have a max in this case A is negative two. So we have a max. So now we're gonna find our vertex so that we can find the maximum Y value. So negative B over two A. Gives us the X. Value of our vertex. And then we're going to evaluate the function F. At negative B over two. A. To give them our maximum y value. So we have negative 5/2 times negative two. Which simplifies to be 5/4. So now we're going to evaluate the function F at 5/4. So we get negative two times 5/4 squared plus five times 5/4 -1. This becomes negative too Over 25/16 Plus 25/4 minus one. So this is negative 50 over. We must simplify that. Uh huh. So too goes into 16 8 times. So this is negative 25/8. So we're gonna multiply this one by two. So we get plus 50 over eight. Gonna multiply these two by eight. So get negative 8/8. So negative 25 plus 50 minus eight gives us 17/8. So this y value is our max weiss or range are all the wise Less than or equal to 17/8. So now we're gonna solve the function negative two X squared plus five x minus one equal to two. So we got negative two X squared plus five x minus remove our three over. I mean are two over. It becomes -3 is equal to zero. We're gonna pull out a negative sign. So we get positive two X squared minus five X plus three is equal to zero. So then we factor we get to X X. And then we get -3 -1. So yeah solve each parentheses equal for zero and so we get to x minus one is equal to zero. So we move this over, we get two. X is equal to one. X is equal to 1/2 And then we get X -3 is equal to zero. So we move this over and we get X is equal to three. So both of these numbers at x equals one half and X equals three gives us a function The function equal to two.

So we're giving a domain and we want to find the range for each function. So our domain is our list of ex values, so we just need to plug those in or X here and get a wide value. But why? Value is really this ethics. It's just written as a function of X. So So I'm gonna put why. So you have y equals to the first point is negative three. So I just put that in. This becomes negative six, and then that becomes negative seven. So you really just audiology bravely as usual. So we have negative two times in a positive two times. Negative one. Do this negative too. Minus one. That gives us the negative three value. Next, we're gonna plug in zero that becomes 00 minus one gives us negative one. The next point is 1.5 since I was 1.5 years. Three and the money's one gives us about you too. And finally we have two times four minus 12 times four is eight and I give us a value of seven so we can run our range in order. So they match Negative seven Negative three Negative one Positive to positive. Seven

Inch of our function. Essentially, we're just going to plug in each point in the domain as our X values and solve for the resulting. Why values. So to make it a little bit more organized, I decided to make a table here and on the left side. We have the values in our domain, and we're going to fill out the right side of our table with the Y values that will correspond to the given X values. So we can start by finding our first why value as a wise equal to X's negative three. So when we put that into the equation, you get negative three minus four over, too, which is going to simplify to negative seven over, too. So I'll fill that in in my table. Our next point will be wise equal to again X's negative one minus four over too. So this is going to reduce to negative five over too. And essentially we're just going to keep finding each of our other values of why, the same way. And so when we do that, our remaining values are going to be negative too negative. Five over four in zero. So our range of our function is just going to be each of these, Uh, why? Points that we saw before. And a set of curly rockets. So our range is negative. Seven over Too negative. Five over. Too negative. Too negative. Five over four ends here.


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