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Use the results of the specified exercises to determine (a) the domain and (b) the range of each function.$y=|x+4|-3$ (Exercise 21)...

Question

Use the results of the specified exercises to determine (a) the domain and (b) the range of each function.$y=|x+4|-3$ (Exercise 21)

Use the results of the specified exercises to determine (a) the domain and (b) the range of each function. $y=|x+4|-3$ (Exercise 21)



Answers

Use the results of the specified exercises to determine (a) the domain and (b) the range of each function. $y=|x+4|-3$ (Exercise 21)

In problem 24 year asked to give the domain a range of the function. Why equals X Squared minus three? And I've gone ahead and graft that using does most because I think it's often easier to tell the domain and range when you have a visual picture of it. Remember that we'll dozens doesn't show this going forever and ever every single axis going to have a course finding why, right? There's nothing that I can't square thinking about this visually way down here. I went forever, never to negative infinity. There is a corresponding point up there, and there are no gaps and holes in that all the way across to positive infinity. All the exes can be put into the function, and you can find a corresponding why value. So the domain goes from negative infinity to positive infinity. No gaps and holes on the graph. No restrictions on what we can put as an input. But the wise are different. The range is a little bit different down here. Negative infinity. I'm not seeing anything. In fact, I'm not getting a value until I hit here. Then everything occurs forever and ever until positive infinity So where did this start? The started down at negative three. So the range is from negative three to infinity. Thinking about that in terms of the equation itself, I know that the X squared part is going to always give me a non negative answer. Right? The smallest one is gonna be 00 square will be zero. Everything else will be greater than that. And zero take away. Three means that the smallest value that I'm going to have is an output is negative. Three again. I think it's easier to see that on the graph.

And problem number 26 we are asked to find the domain and range of the function y equals the opposite of X plus three, and I'm gonna haven't graft this on does most because I think it's usually easier to see the domain arrange when you have a visual image. Um, does most does not draw in that this goes on forever, but we know that it does. So the domain done. Ah, the way down here at negative infinity. There is a corresponding point way up there, right? So there are no gaps or holes in a line as we move from negative infinity to positive infinity. There's going to be an axe that corresponds to a why in each one of those, so the domain goes from negative infinity to infinity Algebraic Lee. That's because every number that I can input for acts I could take the opposite of that. There's no restrictions on the input. Similarly, the range I am finding outputs way down here, and those continue without gaps or holes forever and ever and ever. So the range is also from negative infinity to infinity

FX. It is one developer, two weeks forex less than zero and it is X plus three for ex girlfriend crystal A little So in this case, domain off effects is already a lumber that is minus infinity to plus infinity and range off ethics. It is also all real number as excellent, and Girardi's explosive three and X less than Gerrard is one by two times affects so at zero, it is also giving zero when X is minus 30 So here range is already a lumber, so we can buy it ranges All are and we can hurt minus and fair duplicity.

Is negative one divided by three times X plus two. Four x less any goes to zero and X minus faith when X is good and evil, so it all values off Exit is a linear function. If X is lenient, hence domain off FX is all real number that is minus infinity, rue infinity and range off effects is what, as all ex are included and it is linear functions ranges also all real number that is minus infinity to plus infinity.


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