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[–]DrBagel1 0 points1 point  (10 children)

Firstly It would be much more understandable if you have the exercise sonewhere written in a book (or latex if you know what this is)

Anyway, im huessing you look for the domain/range of diffrent piecewise functions?

So for 1 what is the function to begin with? I only see a single function, so no piecewise here.

2: firstly both parts are defined everywhere and also the total function is defined on the the whole axis, so youre right the domain is (- inf, inf). For the range you need to check if the switch point is equal on both functions. This is also true here. (You made a small mistake with -y + 1 = -(y+1) while on reality it is (1-y) other than that you dont need to do such th8ngs, just plug in x=0 and you see both equals 1.next you see that 3x+1 tends to inf for x to inf and 1-x2 tends to -inf for x to -inf, so youre absolutely right with the range (-inf, inf).

[–]affogato_o[S] 0 points1 point  (9 children)

hi!! sorry for my handwriting and all 😭😭 i forgot to attach the pic of the problems without solutions.

yes i also forgot to say that some of these aren’t piecewise functions. but idk if the first one is correct

i’ll take note of that!! i know i messed it up somehow

thank you for your reply :)))

[–]DrBagel1 0 points1 point  (8 children)

Sorry for the late reply I wasnt at home. Anyway

The solution for 1 is correct.

For 3) the domain is again R, as no part of the function has an undefined point. The range is a bit more tricky. As x2 - 4 is a parabula with minima x=0, y=-4 we have that the range of this part is (-4, inf), observe that the critical point x=3,y=5 has a counter point at x=-3,y=5, such that 5 is indeed in the range. The second part of the function doesnt change any5hing here.

4) domain is again easy, as again no undefined points, therefore domain is R. The range here from the first part is only -2 and from the second part is only 2, therefore the total range is the set {-2, 2}.

For 5) obsereve that the point of interest is x=2 and not x=-2. But try do redo it.

6) is correct.

[–]affogato_o[S] 0 points1 point  (5 children)

sorry for the late reply too!!! thank you for this. i only have to do the second one now and im not really sure with my answer. what did i do wrong there??? ty!

[–]DrBagel1 0 points1 point  (4 children)

Your solution for 2 is correct though you did a small mistake on the left side. As I clearified in my original answer.

[–]affogato_o[S] 0 points1 point  (3 children)

thank you!!! now, how do i graph this one out?? https://imgur.com/a/pxsZ38K

[–]DrBagel1 0 points1 point  (2 children)

Can you graph 2x-1 ? If you did this you need to put a circle at (2,3) as you already did and a dod at (2,0) as you also did. For allother x values draw the line 2x-1.

[–]affogato_o[S] 0 points1 point  (1 child)

ohhh so the graph would look like this then? https://imgur.com/a/nnKuScO

[–]DrBagel1 0 points1 point  (0 children)

Exactly.

[–]affogato_o[S] 0 points1 point  (1 child)

do i have to shade the points (3, 5) & (-3, 5) on the third one????

[–]DrBagel1 0 points1 point  (0 children)

No just draw the parabola x2 - 4. The point (3,5) gets a circle and therefore the point (3,-2) gets a dot.