Question

Part 1: Show the work to solve |x+3| +7 is less than or equal to 10.
Part 2: Describe the graph of the solution in a complete sentence.

Answer 1

first of all welcome to open study @Loujoelou

Answer 2

Thx mathslover.

Answer 3

Anyone?

Answer 4

YA

Answer 5

mod(x+3)=10-7
mod(x+3)=3

Answer 6

K I got that. |x+3| is less than or equal to 3.

Answer 7

solve x+3=3 giving x=0
and x+3=-3 giving x=-6

Answer 8

Oh okay. I was just getting confused cause I thought you had to isolate absolute value, but that's for something else. Thx a ton. How would I describe the graph though?

Answer 9

you know the basic curve of modulus function or should i describe??

Answer 10

Forx=−2,y=|x|=−x=−(−2)=2


Forx=−1,y=|x|=−x=−(−1)=1


Forx=0,y=|x|=x=0


Forx=1,y=|x|=x=1


Forx=2,y=|x|=x=2


The graph of the function is shown here :



Figure 1: The domain of the function is R. Modulus function Modulus function (mf1.gif)

The graph of modulus function is continuous having a corner at x=0. It means that graph is differentiable at all points except at x=0 (we can not draw a tangent at a corner). Since graph is symmetric about y-axis, modulus function is even function. We also see that there are pair of x values for non-zero values of y. This, in turn, means that image and pre-images are not uniquely related. As such, modulus function is not invertible.

It is clear from the graph that the domain of modulus function is "R". However, the function values are only positive values, including zero. Hence, range of modulus function is upper half of the real number set, including zero.


Domain=R


Range=[0,∞)

Answer 11

Oh okay. Thank you very much.

Answer 12

check this image this was the graph of mod(x)
and procedure for that

Answer 13

Oh okay.

Answer 14

any other question

Answer 15

Not right now. Just finished my Alg. II virtual quiz and that was the last question. Gonna do the test soon, but I think I'm good for now.

Answer 16

best of luck

Answer 17

Thx.