Relations and Functions Calculators

Calculators for Functions

Domain and Range

This calculator will:
(1.) Determine the domain of a function.
(2.) Determine the range of a function.
(3.) Write the domain of the function in set notation.
(4.) Write the range of the function in set notation.
(5.) Graph the domain on a number line.
(6.) Graph the range on a number line.

To use the calculator, please:
(1.) Type your function (equation) or expression in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed.
(3.) Copy and paste the function (equation) you typed, into the small textbox of the calculator.
(4.) Click the "Submit" button.
(5.) Check to make sure it is the correct function or expression you typed.
(6.) Review the answer.

Using the Domain and Range Calculator
Type: $p(x) = 2x - 7$ as p(x) = 2 * x - 7
Type: $|1 - 3x|$ as abs(1 - 3 * x)
Type: $g(x) = |5 - x|$ as g(x) = |5 - x|
Type: $f(x) = 3 + \dfrac{9}{x}$ as f(x) = 3 + (9/x)
Type: $\dfrac{x + 2}{2 - x}$ as (x + 2) / (2 - x)
Type: $p(x) = 3x^3 - 2x^2 + 7x - 5$ as p(x) = 3 * x^3 - 2 * x^2 + 7 * x - 5
Type: $\dfrac{5 - x}{x^2 - 3x}$ as (5 - x) / (x^2 - 3 * x)
Type: $g(x) = \sqrt{10 - 7x}$ as g(x) = sqrt(10 - 7 * x)
Type: $f(x) = \sqrt[3]{x + 14} - 2$ as f(x) = cuberoot(x + 14) - 2
Type: $\sqrt[4]{5x + 1}$ as fourthroot(5 * x + 1)

Function:

Evaluate Functions

This calculator will:
(1.) Evaluate a function for a specified value.
(2.) Return the answer in the simplest form.
(3.) Graph the function and indicate the specified value.

To use the calculator, please:
(1.) Assume the function is $f(x)$.
(2.) Type your expression in the first textbox: bigger Textbox 1.
(3.) Type your specified value in the second textbox: bigger Textbox 2.
(4.) Type them according to the examples I listed.
(5.) Delete the default expression in the first textbox of the calculator.
(6.) Delete the default value in the second textbox of the calculator.
(7.) Copy and paste the expression you typed, into the first textbox of the calculator.
(8.) Copy and paste the specified value you typed, into the second textbox of the calculator.
(9.) Click the "Submit" button.
(10.) Check to make sure that the expression and specified value are your questions.
(11.) Review the answer(s). At least one of the answers is what you need.

Using the Evaluating Functions Calculator
Type: $3x^2 - 3x + 1$ as 3 * x^2 - 3 * x + 1
$g(0)$ means x = 0
$g(-2)$ means x = -2
$g(3)$ means x = 3
$g(-x)$ means x = -x
$g(3y)$ means x = 3y
$g(1 - t)$ means x = 1 - t
$g(7 + h)$ means x = 7 + h
Type: $\dfrac{x - 5}{x + 3}$ as (x - 5) / (x + 3)
$p(7)$ means x = 7
$p(-12.75)$ means x = -12.75
$p(-3)$ means x = -3
$p(x + h)$ means x = x + h
$p\left(\dfrac{2}{3} \right)$ means x = 2/3
$p(\sqrt{2})$ means x = sqrt(2)
$p(\sqrt[3]{2})$ means x = cuberoot(2)
Type: $\dfrac{x}{\sqrt{5 - 3x^2}}$ as x / sqrt(5 - 3 *x^2)
$f(\dfrac{1}{3})$ means x = 1/3
$f\left(2x - \dfrac{3 - x}{5x^2}\right)$ means x = 2 * x - (3 / (5 * x^2))
$p\left(\dfrac{3x}{\sqrt{x} + 1} - 7x^3 \right)$ means x = (3 - x) / (sqrt(x) + 1) - (7 * x^3)

Function:

Specified Value:

Arithmetic Operations on Functions

This calculator will:
(1.) Add two functions.
(2.) Subtract two functions.
(3.) Multiply two functions.
(4.) Divide two functions.
(5.) Calculate the result of a function raised to an exponent value.
(6.) Perform arithmetic operations on functions according to the order of operations.
(7.) Graph the result of the arithmetic operation.

To use the calculator, please:
(1.) Assume the first function is $f(x)$.
(2.) Assume the second function is $g(x)$.
(3.) Type the first function in the first textbox: bigger Textbox 1.
(4.) Type the second function in the first textbox: bigger Textbox 2.
(5.) Type the arithmetic operation(s) in the third textbox - bigger Textbox 3.
(6.) Type them according to the examples I listed.
(7.) Copy and paste the first expression you typed, into the first textbox of the calculator.
(8.) Copy and paste the second expression you typed, into the second textbox of the calculator.
(9.) Copy and paste the arithmetic operation(s) you typed, into the third textbox of the calculator.
(10.) Click the "Submit" button.
(11.) Check to make sure that the expressions you typed are the actual expressions of your question.
(12.) Review all the answer(s). At least one of the answers is what you need.

Using the Arithmetic Operations on Functions Calculator
Type:
f(x) = $-4x + 3$ as -4 * x + 3
g(x) = $7x + 5$ as 7 * x + 5
Arithmetic Operation: $f(x) + g(x)$ as f + g
Arithmetic Operation: $f(x) - g(x)$ as f - g
Arithmetic Operation: $f(x) * g(x)$ as f * g
Arithmetic Operation: $f(x) \div g(x)$ as f / g
Arithmetic Operation: $3f(x)^2 - 7g(x)^3$ as 3 * f^2 - 7 * g^3
Type:
f(x) = $3x^2 + 10x - 25$ as 3 * x^2 + 10 * x - 25
g(x) = $x^2 + 4x - 5$ as x^2 + 4 * x - 5
Arithmetic Operation: $f(x) + g(x)$ as f + g
Arithmetic Operation: $f(x) - g(x)$ as f - g
Arithmetic Operation: $f(x) * g(x)$ as f * g
Arithmetic Operation: $f(x) \div g(x)$ as f / g
Arithmetic Operation: $3f(x)^2 - 7g(x)^3$ as 3 * f^2 - 7 * g^3
Type:
f(x) = $\sqrt{1 - 3x}$ as sqrt(1 - 3 * x)
g(x) = $\sqrt[3]{5x^2 + 7x}$ as cuberoot(5 * x^2 + 7 * x)
Arithmetic Operation: $f(x) + g(x)$ as f + g
Arithmetic Operation: $f(x) - g(x)$ as f - g
Arithmetic Operation: $f(x) * g(x)$ as f * g
Arithmetic Operation: $f(x) \div g(x)$ as f / g
Arithmetic Operation: $3\sqrt{2f(x)^2} - 12\sqrt[3]{7g(x)^3}$ as 3 * sqrt(2 * f^2) - 12 * cuberoot(7 * g^3)

$f(x) = $

$g(x) = $

$Arithmetic\: Operation:$

Graph Functions

This calculator will:
(1.) Graph a polynomial function.

To use the calculator, please:
(1.) Type your function/expression in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed.
(3.) Delete the "default" function/expression in the textbox of the calculator.
(4.) Copy and paste the expression you typed, into the small textbox of the calculator.
(5.) Click the "Submit" button.
(6.) Check to make sure that it is the correct function/expression you typed.
(7.) Review the graph.

Using the Graph Functions Calculator
Type: $f(p) = 5p^2 - 25$ as 5 * p^2 - 25
Type: $g(x) = -\dfrac{1}{6} * x^3 - 3x + 7$ as (-1/6)*x^3 - 3 * x + 7
Type: $f(x) = -4.2x^4 + x^6 + 0.1x^7$ as -4.2 * x^4 + x^6 + 0.1 * x^7
Type: $f(x) = 6 + \dfrac{1}{6}x^4 - \dfrac{5}{7}x^3$ as 6 + (1/6) * x^4 - (5/7) * x^3
Type: $h(x) = \sqrt{2}x^3 + 3x^2 - 2x + 2$ as sqrt(2) * x^3 + 3 * x^2 - 2 * x + 2
Type: $f(x) = -3.476x^4 + 35.145x^3 - 97.678x^2 + 41.613x + 178.288$ as -3.476x^4 + 35.145x^3 - 97.678x^2 + 41.613x + 178.288
Type: $f(k) = 7x^3 - x^2 - 448x + 64$ as 7*x^3 - x^2 - 448 * x + 64
Type: $f(x) = (x + 3)^2 (x - 7)$ as (x + 3)^2 * (x - 7)
Type: $f(x) = (x^2 - 4)^5$ as (x^2 - 4)^5
Type: $f(x) = -3(x + 3)(x + 3) (x + 3)(x - 4)$ as -3 * (x + 3)* (x + 3) * (x + 3) * (x - 4)
Type: $f(x) = -8(x - 4)^3(x + 3)^4x^2$ as -8 * (x - 4)^3 * (x + 3)^ 4 * x^2
Type: $f(x) = x^7(2x - 5)^2(7 - 3x)^3$ as x^7 * (2 * x - 5)^2 * (7 - 3 * x)^3

Graph

Symmetry of Functions

This calculator will:
(1.) Determine the symmetry of a function (as indicated by Result: and/or Parity relation: in the output window).
(2.) Determine other details regarding the function.

To use the calculator, please:
(1.) Type your function (equation) or expression in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed.
(3.) Copy and paste the function (equation) you typed, into the small textbox of the calculator.
(4.) Click the "Submit" button.
(5.) Check to make sure it is the correct function or expression you typed.
(6.) Review the answer.

Using the Symmetry of Functions Calculator
Type: $p(x) = 2x - 7$ as p(x) = 2 * x - 7
Type: $|1 - 3x|$ as abs(1 - 3 * x)
Type: $g(x) = |5 - x|$ as g(x) = |5 - x|
Type: $f(x) = 3 + \dfrac{9}{x}$ as f(x) = 3 + (9/x)
Type: $\dfrac{x + 2}{2 - x}$ as (x + 2) / (2 - x)
Type: $p(x) = 3x^3 - 2x^2 + 7x - 5$ as p(x) = 3 * x^3 - 2 * x^2 + 7 * x - 5
Type: $\dfrac{5 - x}{x^2 - 3x}$ as (5 - x) / (x^2 - 3 * x)
Type: $g(x) = \sqrt{10 - 7x}$ as g(x) = sqrt(10 - 7 * x)
Type: $f(x) = \sqrt[3]{x + 14} - 2$ as f(x) = cuberoot(x + 14) - 2
Type: $\sqrt[4]{5x + 1}$ as fourthroot(5 * x + 1)

Function:

Inverse of Functions

This calculator will:
(1.) Determine the inverse of a function.
(2.) Graph the function.
(3.) Graph the inverse of the function.
The function and the inverse of the function are plotted on the same graph.

To use the calculator, please:
(1.) Type your function (equation) or expression in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed.
(3.) Copy and paste the function (equation) you typed, into the small textbox of the calculator.
(4.) Click the "Submit" button.
(5.) Check to make sure it is the correct function or expression you typed.
(6.) Review the answer.

Using the Inverse of Functions Calculator
Type: $p(x) = 2x - 7$ as p(x) = 2 * x - 7
Type: $|1 - 3x|$ as abs(1 - 3 * x)
Type: $g(x) = |5 - x|$ as g(x) = |5 - x|
Type: $f(x) = 3 + \dfrac{9}{x}$ as f(x) = 3 + (9/x)
Type: $\dfrac{x + 2}{2 - x}$ as (x + 2) / (2 - x)
Type: $p(x) = 3x^3 - 2x^2 + 7x - 5$ as p(x) = 3 * x^3 - 2 * x^2 + 7 * x - 5
Type: $f(x) = \sqrt[3]{x + 14} - 2$ as f(x) = cuberoot(x + 14) - 2

Function:

Difference Quotient

This calculator will:
(1.) Calculate the difference quotient of a function.
(2.) Return the answer in the simplest form.

To use the calculator, please:
(1.) Assume the function is $f(x)$.
(2.) Assume the function value is $f(x + h)$.
(3.) Calculate the function value first. Use the "Evaluating Functions Calculator" to calculate it.
Find the value of $f(x + h)$ first using the "Evaluating Functions Calculator".
In other words, evaluate the function, $f(x)$ for $x = x + h$ using the "Evaluating Functions Calculator".
(4.) Type your expression in the first textbox: bigger Textbox 1.
(5.) Type the result (the calculated value you got from the Evaluating Functions Calculator) in the second textbox: bigger Textbox 2.
(6.) Type them according to the examples I listed.
(7.) Copy and paste the expression you typed, into the first textbox of the calculator.
(8.) Copy and paste the calculated value you typed, into the second textbox of the calculator.
(9.) Click the "Difference Quotient" button.
(10.) Check to make sure that those values were correctly substituted in the formula for Difference Quotient.
(11.) Review the answer(s). At least one of the answers is what you need.

Using the Difference Quotient Calculator
Type:
f(x) = $3x - 7$ as 3 * x - 7
From the Evaluating Functions Calculator,
f(x + h) = $3h + 3x - 7$ as 3 * h + 3 * x - 7
Type:
f(x) = $8 - 3x^2$ as 8 - 3 * x^2
From the Evaluating Functions Calculator,
f(x + h) = $8 - 3x^2 - 6xh - 3h^2$ as 8 - 3 * x^2 - 6 * x * h - 3 * h^2
Type:
f(x) = $5x^2 - x - 12$ as 5 * x^2 - x - 12
From the Evaluating Functions Calculator,
f(x + h) = $5x^2 + 10xh + 5h^2 - x - h - 12$ as 5 * x^2 + 10 * x * h + 5 * h^2 - x - h - 12
Type:
f(x) = $\dfrac{x}{x + 1}$ as x / (x + 1)
From the Evaluating Functions Calculator,
f(x + h) = $\dfrac{x + h}{x + h - 1}$ as (x + h) / (x + h - 1)
Type:
f(x) = $\dfrac{-3}{x^2}$ as -3 / x^2
From the Evaluating Functions Calculator,
f(x + h) = $\dfrac{-3}{(x + h)^2}$ as -3 / (x + h)^2

$f(x)$:

$f(x + h)$:

Calculators for Linear Functions and Quadratic Functions

Linear Functions

Given: Slope and a Point that passes through the origin $(0, 0)$

Where: Slope is an integer

To Find: Slope-Intercept Form, Intercepts, Standard Form

Slope =

Point: (, )

Slope-Intercept Form: $y = $ $x + $

Standard Form: $x + $ $y = $

$x$-Intercept = (, )

$y$-Intercept = (, )

Given: Slope and a Point that passes through the origin $(0, 0)$

Where: Slope is a fraction

To Find: Slope-Intercept Form, Intercepts, Standard Form

Slope = ⁄

Point: (, )

Slope-Intercept Form: $y = $ ⁄ $x + $

Standard Form: $x + $ $y = $

$x$-Intercept = (, )

$y$-Intercept = (, )

Given: Slope and a Point $(x_1, y_1)$

Where: The Slope and the co-ordinates of the Point are integers

To Find: Slope-Intercept Form, Intercepts, Standard Form

Please NOTE:

(1.) If any of the answers is a decimal, and you want to convert it to a fraction, please use the calculator in this tab that converts decimals into simplified fractions.
Just copy the entire decimal (without the sign) as is and paste in that calculator.
Then, you can include the sign if it is a negative sign.

Slope =

Point: (, )

Slope-Intercept Form: $y = $ $x + $

Standard Form: $x + $ $y = $

$x$-Intercept = (, )

$y$-Intercept = (, )

Given: Two Points: $(x_1, y_1)$ and $(x_2, y_2)$

Where: The coordinates of the Points are integers

To Find: Slope, Intercepts, Slope-Intercept Form, Standard Form, Point-Slope Form

Please NOTE:

(1.) If none of the $x-coordinates$ of the points is zero, please put the lesser value of $x$ as the $x-coordinate$ of Point $1$ along with it's matching $y-coordinate$ (not necessarily the lesser $y-coordinate$).
(2.) If any of the answers is a decimal, and you want to convert it to a fraction, please use the calculator in this tab that converts decimals into simplified fractions.
Just copy the entire decimal (without the sign) as is and paste in that calculator.
Then, you can include the sign if it is a negative sign.
(3.) If there are any decimals in the Slope-Intercept Form, then the Standard Form will not be correct.
What do you need to do?
Please convert the decimals into simplified fractions.
Then use the appropriate forms in this tab to convert the Slope-Intercept Form to Standard Form

Point 1: (, )

Point 2: (, )

Slope =

Slope-Intercept Form: $y = $ $x + $

Standard Form: $x + $ $y = $

$x$-Intercept = (, )

$y$-Intercept = (, )

Point-Slope Form:
$y - $ $=$ ($x - $ )
OR
$y - $ $=$ ($x - $ )

Decimal to Fraction

Given: A decimal (positive decimals only)
To Convert: to a simplified fraction
$=$

Given: Slope-Intercept Form

Where: Only the slope is a fraction

To Convert to: Standard Form

Slope-Intercept Form: $y = $ ⁄ $x + $

Standard Form: $x + $ $y = $

Given: Slope-Intercept Form

Where: Only the y-intercept is a fraction

To Convert to: Standard Form

Slope-Intercept Form: $y = $ $x + $ ⁄

Standard Form: $x + $ $y = $

Given: Slope-Intercept Form

Where: The slope and the y-intercept are fractions

and

Where: Both fractions have the same denominator

To Convert to: Standard Form

Slope-Intercept Form: $y = $ ⁄ $x + $ ⁄

Standard Form: $x + $ $y = $

Given: Slope-Intercept Form

Where: The slope and the y-intercept are fractions

and

Where: Both fractions do not have the same denominator

To Convert to: Standard Form

Slope-Intercept Form: $y = $ ⁄ $x + $ ⁄

Standard Form: $x + $ $y = $

Quadratic Functions

Decimal to Fraction

Given: A decimal (positive decimals only)
To Convert: to a simplified fraction
$=$

Given: Table of Some Values for a Quadratic Function (Integers and/or Decimals only)

To Determine: The Quadratic Function and other details

$x$	$y$

Quadratic Function: $y = $ $x^2 + $ $x + $

The function has a value

Vertex = (, )
Based on the Vertex, this means that:
The value at which the extrema value occurs is: and the extrema value is:

$x$-Intercepts = (, ) and (, )

The value of (, )

Optional:

If you did not enter any value before clicking the Calculate button (initially):
(1.) By default, the blank textboox has a value of $0$ (not visible) when the other corresponding value was calculated.
(2.) Please enter a value for either the $x$ or the $y$
(3.) Click the Calculate button to see the corresponding other value.

When $x =$ , $y =$

$x-values =$ and , When $y =$

Given: Table of Some Values for a Quadratic Function (Integers and/or Decimals only)

To Determine: The Quadratic Function and Other Values

Please:
(1.) First: Type each $x$ value and the corresponding $y$ value for three points.
(2.) Second: Type each $x-value$ on a new line. No commas. No spaces. No period. No extra line(s).
(3.) Third: Drag the textarea for the $x$ column by the bottom right corner to enter and see all the $x-values$
(4.) Fourth: Click the Calculate button to see the corresponding $y$ values as well as the quadratic function.
(5.) Fifth: Drag the textarea for the $y$ column by the bottom right corner to see all the $y-values$

$x$	$y$

Quadratic Function: $y = $ $x^2 + $ $x + $

Given: A Quadratic Function

To Determine: Table of Values and other details

Please:
(1.) First: Type the coefficients and the constant of the Quadratic Function.
(2.) Second: Type each $x-value$ on a new line. No commas. No spaces. No period. No extra line(s).
(3.) Third: Drag the textarea for the $x$ column by the bottom right corner to enter and see all the $x-values$
(4.) Fourth: Click the Calculate button to see the corresponding $y$ values as well as the quadratic function.
(5.) Fifth: Drag the textarea for the $y$ column by the bottom right corner to see all the $y-values$

Quadratic Function: $y = $ $x^2 + $ $x + $

The function has a value

Vertex = (, )
Based on the Vertex, this means that:
The value at which the extrema value occurs is: and the extrema value is:

$x$-Intercepts = (, ) and (, )

$y$-Intercept = (, )

Given: A Quadratic Function in Standard Form

To Determine: The Quadratic Function in Vertex Form and other details

Standard Form of Quadratic Function: $y = $ $x^2 + $ $x + $

The function has a value

Vertex Form of Quadratic Function: $y = $ ($x -$ )$^2 +$

Vertex = (, )
Based on the Vertex, this means that:
The value at which the extrema value occurs is: and the extrema value is:

$x$-Intercepts = (, ) and (, )

$y$-Intercept = (, )

TI-84 Graphing Calculator

Make a Table of Values, Graph and Trace Functions Using the TI-84 Calculator

This calculator will:
(1.) Form a Table of Values.
(2.) Graph equations/functions.
(3.) Trace functions.
(4.) Displays the Table of Values and the Graph in the same window.

To use the calculator, please:
(1.) Visit the link: TI-84 Calculator
(2.) Click the "Graphing" folder.
(3.) Click the link of "whatever you want to do".
(4.) Follow the directions as illustrated by the "blinking light".