Question

sketch the graph of piece-wise function given by
y=x+1 if x0 and find the domain and range please help me guys?

Answer 1

do you know how to graph y = x+1 without worrying about restrictions?

Answer 2

what do you mean about worrying about restriction sir?

Answer 3

do you know how to graph y = x+1 on a coordinate grid?

Answer 4

yes sir

Answer 5

using vertex

Answer 6

this is a linear equation. There is no vertex

Answer 7

using (h,k) formula

Answer 8

focus on y = x+1 for now. This is linear. There is no vertex

Answer 9

the graph pf x+1 is x=0 and y=1 I am right or wrong?

Answer 10

(0,1) is one point on this line. Yes

Answer 11

what's another point?

Answer 12

x^2+2 where x=0 and y=2

Answer 13

if you plugged x = 1 into y = x+1, what is the value of y?

Answer 14

y=2

Answer 15

when x = 1, y = 2
put those together and (1,2) is another point on the graph of y = x+1

Answer 16

plot (0,1) and (1,2). Draw a straight line through them

The line would normally go off forever in both directions; however, there's a restriction on x

it says that y = x+1 if x <= 0

so y = x+1 is only graphed if x is 0 or smaller. Otherwise, you don't graph

Answer 17

i want to see the final graph would you please draw it?

Answer 18

Here's y = x+1 normally. See attached

Answer 19

Here is y = x+1 when you apply the restriction

see attached

notice how there is a closed circle at the endpoint (to indicate we include this point)

Answer 20

here what i did before but my teacher wrong me.

Answer 21

how about the complete graph sir i want to see?

Answer 22

help me please :( ? i want to learn

Answer 23

this is what the full piecewise function would look like. See attached

Answer 24

let me know if that helps or not

Answer 25

now i know why im wrong because i shade the blue one instead of open circle :D

Answer 26

how about the domain and range sir?

Answer 27

hopefully you can see how the domain is the set of all real numbers? Notice how we can pick any x value and it leads to a point on the graph

Answer 28

how about the range sir is a set of real number but not equal to 2?

Answer 29

we can do almost every real number for the range, but there's a gap from y = 1 to y = 2

Answer 30

we can say that the range is the set of y values such that \(\Large y \le 1\) or \(\Large y > 2\)