SOLUTION: What is the vertex of the graph of y = |2x - 3| - 5? What is the range of the function? I have tried to graph the given equation and found it to be a straight diagonal line. So

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Question 234239: What is the vertex of the graph of y = |2x - 3| - 5? What is the range of the function?
I have tried to graph the given equation and found it to be a straight diagonal line. So my solution/answer to the problems are: a.) no solution for the vertex
b.) range is infinite.
Am I right with my answers? I would appreciate it very much if you could show me the step by step solution and the correct answer to the above problems. Please... thanks and God bless.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
What is the vertex of the graph of y = |2x - 3| - 5? What is the range of the function?
You should be able to recognize that the value inside the absolute has to be positive or 0,
therefore the the range (y) has to be - 5 or greater, right?
:
Plot a couple points here
x = -3
y = |2(-3) - 3| - 5
y = |-6 - 3| - 5
y = |-9| - 5
Remove the absolutes
y = 9 - 5
y = +4
Plot x/y point -3, +4
:
Plot the value so that the value inside the absolute = 0
x = 1.5
y = |2(1.5) - 3| - 5
y = |3 - 3| - 5
y = 0 - 5
y = -5
Plot point x/y : 1.5, -5, the minimum range
;
x = +3
y = |2(3) - 3| - 5
y = |6-3| - 5
y = 3 -5
y = -2
Plot points x/y +3, -2
:
Looks like this: