SOLUTION: Graph each absolute value function and state its domain and range y=|2x-3| and x+3=|y|

Algebra ->  Absolute-value -> SOLUTION: Graph each absolute value function and state its domain and range y=|2x-3| and x+3=|y|      Log On


   

Question 924258: Graph each absolute value function and state its domain and range
y=|2x-3|
and
x+3=|y|
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This response is not a complete answer or solution but may be helpful.

The first equation will be only positive for any values of/ or all values of x. y=abs%282x-3%29 range is The Real Numbers greater than or equal to zero. The Domain is all real numbers. The critical x value at which sharp point corner occurs is x=3%2F2.

Your second given equation can be also expressed, sqrt%28y%5E2%29=x%2B3. This lets you find y%5E2=%28x%2B3%29%5E2. Take square root of both sides gives you two branches:
y=-sqrt%28%28x%2B3%29%5E2%29 and y=sqrt%28%28x%2B3%29%5E2%29;
Finishing this,
highlight%28y=-%28x%2B3%29%29 OR highlight%28y=x%2B3%29.
BUT look very carefully at the original equation again.
The right member is never negative. This means for DOMAIN, x%3E=-3.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=abs%282x-3%29
find several points, make table,plot points, and graph the function
x|y
-3|9.....y=abs%282%28-3%29-3%29=abs%28-6-3%29=abs%28-9%29=9
-2|7.....y=abs%282%28-2%29-3%29=abs%28-4-3%29=abs%28-7%29=7
-1|5.....y=abs%282%28-1%29-3%29=abs%28-2-3%29=abs%28-5%29=5
0|3.....y=abs%282%280%29-3%29=abs%280-3%29=abs%28-3%29=3
1|1.....y=abs%282%281%29-3%29=abs%282-3%29=abs%28-1%29=1
2|1.....y=abs%282%282%29-3%29=abs%284-3%29=abs%281%29=1
3|3.....y=abs%282%283%29-3%29=abs%286-3%29=abs%283%29=3
5|7.....y=abs%282%285%29-3%29=abs%2810-3%29=abs%287%29=7
plot these points and graph:


domain:
R (all real numbers)
range:
{ y element R : y%3E=0 } (all non-negative real numbers)

2.
x%2B3=abs%28y%29=> x%2B3+=+sqrt%28y%5E2%29=> x%2B3+=+y or x%2B3+=+-y
x%2B3+=+y
x%2B3+=+-y=>-x-3+=+y

x|y
-3|0.....abs%28y%29=x%2B3=-3%2B3=0
-2|1.....abs%28y%29=x%2B3=-2%2B3=1=>y=1 or y=-1
-2|-1
-1|2.....abs%28y%29=x%2B3=-1%2B3=2=>y=2 or y=-2
-1|-2
0|3.....abs%28y%29=x%2B3=0%2B3=3=>y=3 or y=-3
0|-3
1|4.....abs%28y%29=x%2B3=1%2B3=4=>y=4 or y=-4
1|-4
5|8.....abs%28y%29=x%2B3=5%2B3=8=>y=8 or y=-8
5|-8


domain:
R%5E2
range:
unable to determine range
Re%28x%29%3E-3