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Let f(x) = | x | be the absolute value function.
1. Why is the range of this function {y | y >= 0}?
2. Why does this function have an absolute minimum of 0 at x = 0?
Can the answer be that (-infinity, 0) and (0, infinity) meet at the origin where x = 0?
The greatest truth about the Rapture is not its timing but it's reality.
Dr. David Jeremiah
Online
Have you tried looking at the graph?
For positive x the graph is the same as y = x.
For negative x the graph is the same as y = -x
So, putting these together, you get a V shaped graph with the origin at the bottom of the V.
Your last line suggests you're looking at a different graph. ( y = 1/x maybe)
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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Have you tried looking at the graph?
For positive x the graph is the same as y = x.
For negative x the graph is the same as y = -x
So, putting these together, you get a V shaped graph with the origin at the bottom of the V.
Your last line suggests you're looking at a different graph. ( y = 1/x maybe)
Bob
I was looking at the V-shape graph before posting this question (unless my eyes wondered away from the absolute value function to the reciprocal function). In any case, I need extra practice finding the domain range of graphs.
The greatest truth about the Rapture is not its timing but it's reality.
Dr. David Jeremiah
Online
Extra practice.
(1) y = x^2
(2) y = x^3 - 2x
(3) y = x^2/(x+4)
(4) y = sqrt(100-x^2)
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
Extra practice.
(1) y = x^2
(2) y = x^3 - 2x
(3) y = x^2/(x+4)
(4) y = sqrt(100-x^2)
Bob
Ok. I will work on these and show my effort here.
The greatest truth about the Rapture is not its timing but it's reality.
Dr. David Jeremiah
Online
Extra practice.
(1) y = x^2
(2) y = x^3 - 2x
(3) y = x^2/(x+4)
(4) y = sqrt(100-x^2)
Bob
For y = x^2
Vertex = (0, 0) = absolute minimum
Range = all non-negative real numbers
Domain = all real numbers
No absolute maximum.
For y = x^3 - 2x
Range = Domain = all real numbers.
No absolute minimum.
No absolute maximum.
For y = (x^2)/(x + 4)
Domain = all real numbers except x cannot be -4.
This function is not one to one. So, it does not have an inverse.
I say no range.
I an not sure about absolute minimum and absolute maximum values.
For y = sqrt{100 - x^2}
Domain: -10 <= x <= 10
Range: 0 <= y <= 10
Absolute maximum at the point (0, 10).
No absolute minimum.
You say?
The greatest truth about the Rapture is not its timing but it's reality.
Dr. David Jeremiah
Online
Excellent attempt. 3/4 perfect. Number 3 is very tricky. Without a graph I'd have difficulty. It's the range that you need to work on. I recommend using the grapher.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
Excellent attempt. 3/4 perfect. Number 3 is very tricky. Without a graph I'd have difficulty. It's the range that you need to work on. I recommend using the grapher.
Bob
I will try 3 again.
The greatest truth about the Rapture is not its timing but it's reality.
Dr. David Jeremiah
Online
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