Question 255156: please just help me with these two problems I am so confused... but so happy my dad found this website!! I graphed these twice and got a line and when I did it wrong I made my own V shape on the Y axis on purpose.
Thanks!
4. y=|-3x|
40. y=-|x-3|
I have way more problems but I'm hoping if a professional shows me how to do it that well... I might understand it or get how to do this for my other problems. Thanks again!!
Found 2 solutions by dabanfield, Edwin McCravy:
Answer by dabanfield(803)   (Show Source):
You can put this solution on YOUR website! 4). y=|-3x|
40). y=-|x-3|
Remember the definition of absolute value:
|a| = a if a>=0
|a| = -a if a<0
So for #4 above we have y = -3x when -3x >= 0 and y = -(-3x) = 3x when -3x < 0. Dividing both sides of these inequalities by -3 and reversing the sign of the inequalities (because we are dividing by a negative) we have -3x >= 0 if and only if x < 0. Similarly -3x < 0 if and only if x>=0.
So we have:
the line y = -3x when x <= 0 and
the line y = 3x when x > 0
These are two "half" iines which form a "V" with the low point at (0,0) and opening upward around the y-axis.
#40 is very similar. The "V" is shifted to the right to the point (3,0) and opens downward.
I hope this helps.
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website! y=|-3x|
First find the VERTEX by taking what's between the absolute
value bars and putting it equal to zero:
-3x = 0
Divide both sides by -3
x = 0
Substitute this in the original equation:
y = |-3(0)|
y = |0|
y = 0
So plot the point (0,0). That happens to be the origin:
Next choose one value of x less than 0 which will give a point
on the left of the vertex, then choose another value of x greater
than 0 which will give a point on the right of the vertex:
For the point on the left of the vertex, we choose x=-1. Substitute
it in the original equation:
y = |-3x|
y = |-3(-1)|
y = |3|
y = 3
That gives you the point (-1,3) which is left of the vertex.
Next choose one value of x greater than 0 which will give a point
on the right of the vertex.
For the point on the right of the vertex, we choose x=+1. Substitute
it in the original equation:
y = |-3x|
y = |-3(+1)|
y = |-3|
y = 3
That gives you the point (1,3) which is right of the vertex.
Plot those points:
Draw the v-shaped graph:
40. y=-|x-3|
First find the VERTEX by taking what's between the absolute
value bars and putting it equal to zero:
x-3 = 0
Add +3 to both sides:
x = 3
Substitute this in the original equation:
y = -|(3)-3|
y = -|0|
y = 0
So plot the point (3,0)
Next choose one value of x less than 3 which will give a point
on the left of the vertex, then choose another value of x greater
than 3 which will give a point on the right of the vertex:
For the point on the left of the vertex, we choose x=2. Substitute
it in the original equation:
y = -|x-3|
y = -|(2)-3|
y = -|2-3|
y = -|-1|
y = -(1)
y= -1
That gives you the point (2,-1) which is left of the vertex.
Next choose one value of x greater than 3 which will give a point
on the right of the vertex.
For the point on the right of the vertex, we choose x=4. Substitute
it in the original equation:
y = -|x-3|
y = -|(4)=3|
y = -|4-3|
y = -|1|
y = -1
That gives you the point (4,-1) which is right of the vertex.
Plot those points:
Draw the v-shaped graph:
Edwin
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