Question about Texas Instruments TI-84 Plus Silver Edition Graphic Calculator

**The calculator cannot determine that for you**. But if you enter a value outside the domain it will display an error message

Let there be a function y=f(x).

The domain of the function is the set of values that x is allowed to take. For example, the domain of the f(x)=x^2 is the whole of the real line: any real value you might think of has a square.

The range of a function is the set of all values that the function can take. For f(x)=x^2 the range is [0, infinity[

Posted on Oct 16, 2013

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Posted on Jan 02, 2017

Domain and range are concepts that many students have trouble with, so you are not alone!

Domain is the x values of the relation.

Range is the y values of the relation.

If you have trouble remembering which one is which , like I do, D comes before R, just like x comes before y;)

To determine if a relation is a function, there are several tests that you can use. For every x value, there can be one and only one y value. If there is more than one y value for any x value, it is not a function.

Another test is the vertical line test. If a vertical line only goes through one point on the line, it is a function. If it goes through two points on the line, it is not a function.

As an example, let's look at y = (x-3)^2 + 6.

This parabola is in the form, y=a(x-h)^2 + k, where a indicates a stretch or compression, and whether the parabola opens up or down. If a is positive, it opens up, and the y value of the vertex represents a minimum. If a is negative, it opens down, and the y value of the vertex is a maximum. The values h and k are the x and y values of the vertex.

In this case, a is one, so the parabola opens up, with a minimum value of 6.''

Now back to the domain and range.

Since we can use any value for x in the equation, for the domain, x is an element of real numbers, sometimes written (xER).

For the range, y can only be greater than or equal to the minimum. So the range is y is an element of all real numbers, such that y is greater or equal to 6, sometimes written (yER'y>=6). Sorry I couldn't find the greater than or equal to character;)

Good luck.

Paul

Domain is the x values of the relation.

Range is the y values of the relation.

If you have trouble remembering which one is which , like I do, D comes before R, just like x comes before y;)

To determine if a relation is a function, there are several tests that you can use. For every x value, there can be one and only one y value. If there is more than one y value for any x value, it is not a function.

Another test is the vertical line test. If a vertical line only goes through one point on the line, it is a function. If it goes through two points on the line, it is not a function.

As an example, let's look at y = (x-3)^2 + 6.

This parabola is in the form, y=a(x-h)^2 + k, where a indicates a stretch or compression, and whether the parabola opens up or down. If a is positive, it opens up, and the y value of the vertex represents a minimum. If a is negative, it opens down, and the y value of the vertex is a maximum. The values h and k are the x and y values of the vertex.

In this case, a is one, so the parabola opens up, with a minimum value of 6.''

Now back to the domain and range.

Since we can use any value for x in the equation, for the domain, x is an element of real numbers, sometimes written (xER).

For the range, y can only be greater than or equal to the minimum. So the range is y is an element of all real numbers, such that y is greater or equal to 6, sometimes written (yER'y>=6). Sorry I couldn't find the greater than or equal to character;)

Good luck.

Paul

Oct 03, 2014 | Office Equipment & Supplies

No calculator can give you the domain of definition not the range of values. You must study the function to determine the x-values where the function is not defined. If for some value of x the function is undefined (for example a denominator because 0) then that x-value does not belong to the domain of definition.

One the domain is known, the range can then be determined.

One the domain is known, the range can then be determined.

Sep 07, 2014 | Office Equipment & Supplies

Once you choose the domain of a function, you cannot restrict its range. ** It depends on the domain of definition.** You can however restrict the window within which you look at the graph. Change the Ymin, Ymax values.

Apr 16, 2014 | Texas Instruments Office Equipment &...

The arccosine function is defined for arguments in the range -1 to +1. -125.85/-120.36 is larger than 1 and hence outside the domain of the arccosine function.

Dec 03, 2013 | Texas Instruments TI-84 Plus Calculator

For y = 2x-3, both range and domain are from -infinity to +infinity.
If you wanna read more about it, please open the following link:
http://www.intmath.com/functions-and-graphs/2a-domain-and-range.php

Jul 06, 2011 | Cell Phones

Here is an absurd example of a piecewise function

Y1=11 for X less than 10

Y1=3 for X in the range [10, 20[

Y1=X+5 for X in the range [20, 30[

Y1=10 for X larger than 30

Here is the screen capture of the Y= editor window.

You have

You can use the logical AND operator in the definition of the limits of a domain. See screen capture below.

Y1=11 for X less than 10

Y1=3 for X in the range [10, 20[

Y1=X+5 for X in the range [20, 30[

Y1=10 for X larger than 30

Here is the screen capture of the Y= editor window.

You have

- the definition of the function within a domain, enclosed in () followed by the domain enclosed in ()
- a + to introduce the second piece (definition) (domain)
- + a third piece (definition ) (domain)
- and so on.
- Use the [2nd][TEST] key sequence to access the relational operators, less than, greater than, etc.

You can use the logical AND operator in the definition of the limits of a domain. See screen capture below.

Jan 20, 2011 | Texas Instruments TI-84 Plus Calculator

Since you are familiar with sines, cosines, you know that their ranges (interval of values) varies from -1 to 1. The inverse functions of sine and cosine tkae their values in that very domain, [-1,1].

However you fed the arc sine function (sin^-1) a vlaue of (25/20.48) and that value is obviously larger outside the [-1,1] domain, hence the DOMAIN error message.

No such domain limitations exist for arc tangent (tan^-1) because the range of the tangent function spans the open interval ]negative infinity to positive infinity[.

However you fed the arc sine function (sin^-1) a vlaue of (25/20.48) and that value is obviously larger outside the [-1,1] domain, hence the DOMAIN error message.

No such domain limitations exist for arc tangent (tan^-1) because the range of the tangent function spans the open interval ]negative infinity to positive infinity[.

Nov 02, 2010 | Texas Instruments TI-84 Plus Silver...

Here is an asurd example of a piecewise function

Y1=11 for X less than 10

Y1=3 for X in the range [10, 20[

Y1=X+5 for X in the range [20, 30[

Y1=10 for X larger than 30

Here is the screen capture of the Y= editor window.

You have

Y1=11 for X less than 10

Y1=3 for X in the range [10, 20[

Y1=X+5 for X in the range [20, 30[

Y1=10 for X larger than 30

Here is the screen capture of the Y= editor window.

You have

- the definition of the function within a domain, enclosed in () followed by the domain enclosed in ()
- a + to introduce the second piece (definition) (domain)
- + a third piece (definition ) (domain)
- and so on.
- Use the [2nd][TEST] key sequence to access the relational operators, less than, greater than, etc.

Mar 09, 2010 | Texas Instruments TI-84 Plus Calculator

Feb 26, 2010 - I was right to suggest to
you to read the page on domain and range of functions: it would have
clarified the concepts to you.

The domain of the sine function is from -infinity to + infinity. But since the function is periodic, with a period equal to 2Pi, by limiting the DOMAIN of values to -1*Pi to +1*PI you see all there is to see. All the rest can be obtained by translation of the curve.

The RANGE of the sine function is LIMITED to values in the interval [-1, 1]

Let us summarize: The DOMAIN of the sine function is ]-infinity, +infinity[ and its RANGE is [-1,+1].

That being said, there is something I would like to point to you

These are the numbers.

You want a "square", so be it. Here is the window setting

and the corresponding picture. Does it look like a square?

Why do you insitst on drawing a square? Horizontally you have the angle ( a number with a unit), while vertically you have a ratio of two lengths ( a pure number). Would even think about a square if you drew your sine function with the degree as angle unit. Horizontally you would have a domain [-180 degrees, 180 degrees] while vertically you have a range [-3.14..., +3.14...]. How can that be a square?

I showed you how you can fix every dimension in the graph window (see the first picture) . Choose any values that you believe will give you a square graph. And I do mean to say "that make you believe", because there is no meaning attached to the "fact" that the window looks like a square. An angle cannot be compared to a the projection of one side of a right triangle onto the hypotenuse.

The domain of the sine function is from -infinity to + infinity. But since the function is periodic, with a period equal to 2Pi, by limiting the DOMAIN of values to -1*Pi to +1*PI you see all there is to see. All the rest can be obtained by translation of the curve.

The RANGE of the sine function is LIMITED to values in the interval [-1, 1]

Let us summarize: The DOMAIN of the sine function is ]-infinity, +infinity[ and its RANGE is [-1,+1].

That being said, there is something I would like to point to you

These are the numbers.

You want a "square", so be it. Here is the window setting

and the corresponding picture. Does it look like a square?

Why do you insitst on drawing a square? Horizontally you have the angle ( a number with a unit), while vertically you have a ratio of two lengths ( a pure number). Would even think about a square if you drew your sine function with the degree as angle unit. Horizontally you would have a domain [-180 degrees, 180 degrees] while vertically you have a range [-3.14..., +3.14...]. How can that be a square?

I showed you how you can fix every dimension in the graph window (see the first picture) . Choose any values that you believe will give you a square graph. And I do mean to say "that make you believe", because there is no meaning attached to the "fact" that the window looks like a square. An angle cannot be compared to a the projection of one side of a right triangle onto the hypotenuse.

Feb 25, 2010 | Casio CFX-9850G Plus Calculator

Graph the function over the domain [-Pi,+Pi]

Then press the [SHIFT][MENU] (SETUP) and in option [Dual Screen] select [G to T] Graph to table. The screen will be spilt in two, but the Table part remains empty.

Press [SHIFT][F1] (TRACE), the cross hair appears on screen.

Move it around on the curve

If you press [EXE] at a cross hair location, the table records the X and Y value. On the following screen capture, the exponential function is graphed along with sin(X) and the table is populated by selected values of the exponential.

Now rate all the solutions I provided for you

Feb 25, 2010 | Casio CFX-9850G Plus Calculator

Jul 21, 2014 | Texas Instruments TI-84 Plus Silver...

Jun 14, 2014 | Texas Instruments TI-84 Plus Silver...

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