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Is it possible to graph functions with restricted domains!

 

For example, can I graph the parent function of a quadratic only when x is greater than or equal to 0?

Guest Dec 5, 2017

Best Answer 

 #1
avatar+1493 
+1

Yes, it is possible. After "Y1=" command line, input \(x^2/(x\geq0)\).

 

Let me explain how this works, so you understand, and you don't just use rote memorization. To access the inequality symbols, press, in order, the blue second button followed by the button reading "math."

 

Upon doing the steps above, your interface should look like the following:

 

TEST  LOGIC

1: =

2: ≠

3: >

4: ≥

5: <

6: ≤

 

Use your directional arrows to navigate to the individual inequalities symbols. 

 

Another skill you must know how to do is storing values as variables. Use this syntax as a guideline for you.

 

[number]→[variable]

 

Let's perform some extremely simple logic calculations with the calculator. 

 

1. Input 10→X on the homescreen command line. 

2. Input X≥0 on the homescreen command line.

 

What did the calculator output? That's right! The calculator outputted a 1. This is the calculator method of saying "true." Now, let's perform another experiment. It is nearly the same process as before.

 

1. Input -10→X on the homescreen command line. 

2. Input X≥0 on the homescreen command line.

 

The calculator outputted a "0" this time to signify a false statement. An interesting fact about this output is that you can also do arithmetic with this information, too. Syntax is extremely important here, so use parentheses even if you think it is completely unnecessary.

 

1. Input 9*(X≥0)+4

 

The calculator outputted 4. How did it do that, you ask? Well, let me explain.

 

\(9*\textcolor{red}{(x\geq0)}+4\)The calculator first evaluates inside of the parentheses so that it adheres to the order of operations.
\(\textcolor{red}{9*0}+4\)Of course, x is set to be equal to -10, so the calculator outputs a "0" because \(-10\ngeq0\). Now, the calculator continues like normal. It, of course, does multiplication first.
\(\textcolor{red}{0+4}\)Now, the calculator adds.
\(4\) 
  

 

So, how does this help me understand what occurs for the restricted domain? Well, let's look at it. Let's pick a number that is less than 0. I'll choose -2, in this case.

 

\(y_1=x^2/(x\geq0)\)Since x=-2, substitute that in for every value of x.
\(y_1=(-2)^2/(-2\geq 0)\) 
\(y_1=4/0\)Uh oh! Dividing by zero causes an error, so this point is not graphed!
  

 

Now, let's try plugging in 2.

 

\(y_1=x^2/(x\geq0)\)Replace every instance of x with a 2.
\(y_1=2^2/(2\geq 0)\)Now, evaluate.
\(y_1=4/1\)Notice how this does not cause a problem because dividing by 1 does not actually affect the output of the function.
\(y_1=4\)The calculator would then plot that point. The process continues.

 

The moral here is that a false statement causes a division by zero error while a true statement leaves the original function untouched.

TheXSquaredFactor  Dec 6, 2017
edited by TheXSquaredFactor  Dec 6, 2017
Sort: 

1+0 Answers

 #1
avatar+1493 
+1
Best Answer

Yes, it is possible. After "Y1=" command line, input \(x^2/(x\geq0)\).

 

Let me explain how this works, so you understand, and you don't just use rote memorization. To access the inequality symbols, press, in order, the blue second button followed by the button reading "math."

 

Upon doing the steps above, your interface should look like the following:

 

TEST  LOGIC

1: =

2: ≠

3: >

4: ≥

5: <

6: ≤

 

Use your directional arrows to navigate to the individual inequalities symbols. 

 

Another skill you must know how to do is storing values as variables. Use this syntax as a guideline for you.

 

[number]→[variable]

 

Let's perform some extremely simple logic calculations with the calculator. 

 

1. Input 10→X on the homescreen command line. 

2. Input X≥0 on the homescreen command line.

 

What did the calculator output? That's right! The calculator outputted a 1. This is the calculator method of saying "true." Now, let's perform another experiment. It is nearly the same process as before.

 

1. Input -10→X on the homescreen command line. 

2. Input X≥0 on the homescreen command line.

 

The calculator outputted a "0" this time to signify a false statement. An interesting fact about this output is that you can also do arithmetic with this information, too. Syntax is extremely important here, so use parentheses even if you think it is completely unnecessary.

 

1. Input 9*(X≥0)+4

 

The calculator outputted 4. How did it do that, you ask? Well, let me explain.

 

\(9*\textcolor{red}{(x\geq0)}+4\)The calculator first evaluates inside of the parentheses so that it adheres to the order of operations.
\(\textcolor{red}{9*0}+4\)Of course, x is set to be equal to -10, so the calculator outputs a "0" because \(-10\ngeq0\). Now, the calculator continues like normal. It, of course, does multiplication first.
\(\textcolor{red}{0+4}\)Now, the calculator adds.
\(4\) 
  

 

So, how does this help me understand what occurs for the restricted domain? Well, let's look at it. Let's pick a number that is less than 0. I'll choose -2, in this case.

 

\(y_1=x^2/(x\geq0)\)Since x=-2, substitute that in for every value of x.
\(y_1=(-2)^2/(-2\geq 0)\) 
\(y_1=4/0\)Uh oh! Dividing by zero causes an error, so this point is not graphed!
  

 

Now, let's try plugging in 2.

 

\(y_1=x^2/(x\geq0)\)Replace every instance of x with a 2.
\(y_1=2^2/(2\geq 0)\)Now, evaluate.
\(y_1=4/1\)Notice how this does not cause a problem because dividing by 1 does not actually affect the output of the function.
\(y_1=4\)The calculator would then plot that point. The process continues.

 

The moral here is that a false statement causes a division by zero error while a true statement leaves the original function untouched.

TheXSquaredFactor  Dec 6, 2017
edited by TheXSquaredFactor  Dec 6, 2017

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