- 1 Is a horizontal line a function?
- 2 What does a function look like written?
- 3 Is a vertical line always a function?
- 4 What makes a function a function?
- 5 What makes it not a function?
- 6 What are the rules for functions?
Is a horizontal line a function?
$\begingroup$ Yup. It represents a function that gives the same output no matter what input you give it. Usually written as $f(x)=a$ (so, for instance, $f(x)=5$ is one such function), and called a constant function, answered Mar 13, 2017 at 7:39 Arthur Arthur 195k 14 gold badges 171 silver badges 303 bronze badges $\endgroup$ 2
$\begingroup$ and what’s the domain of it? $\endgroup$ Mar 13, 2017 at 7:44 $\begingroup$ @Steve Whatever you want it to be. For each domain and each codomain and each point / element in the codomain, there is exactly one constant function with that domain, codomain and output value. $\endgroup$ Mar 13, 2017 at 7:57
$\begingroup$ A horizontal line represents a function (constant function). It is the case that a function can have the same value for many different $x$ inputs. It passes the vertical line test. A function cannot have have $2$ values of $y$ for the same $x$ but The horizontal line has one $y$ value for every $x$, answered Sep 10, 2022 at 19:44 $\endgroup$ 2
$\begingroup$ Welcome to MSE. No, a horizontal line is not a function. It is the graph of a function. $\endgroup$ Sep 10, 2022 at 20:03 $\begingroup$ As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center, $\endgroup$ Sep 10, 2022 at 20:04
What does a function look like written?
Using Function Notation – Once we determine that a relationship is a function, we need to display and define the functional relationships so that we can understand and use them, and sometimes also so that we can program them into computers. There are various ways of representing functions.
A standard function notation is one representation that facilitates working with functions. To represent “height is a function of age,” we start by identifying the descriptive variables \(h\) for height and \(a\) for age. The letters \(f\), \(g\),and \(h\) are often used to represent functions just as we use \(x\), \(y\),and \(z\) to represent numbers and \(A\), \(B\), and \(C\) to represent sets.
\ Remember, we can use any letter to name the function; the notation \(h(a)\) shows us that \(h\) depends on \(a\). The value \(a\) must be put into the function \(h\) to get a result. The parentheses indicate that age is input into the function; they do not indicate multiplication.
- We can also give an algebraic expression as the input to a function.
- For example \(f(a+b)\) means “first add \(a\) and \(b\), and the result is the input for the function \(f\).” The operations must be performed in this order to obtain the correct result.
- Function Notation The notation \(y=f(x)\) defines a function named \(f\).
This is read as “\(y\) is a function of \(x\).” The letter \(x\) represents the input value, or independent variable. The letter \(y\), or \(f(x)\), represents the output value, or dependent variable. Example \(\PageIndex \): Using Function Notation for Days in a Month Use function notation to represent a function whose input is the name of a month and output is the number of days in that month.
Solution Using Function Notation for Days in a Month Use function notation to represent a function whose input is the name of a month and output is the number of days in that month. The number of days in a month is a function of the name of the month, so if we name the function \(f\), we write \(\text =f(\text )\) or \(d=f(m)\).
The name of the month is the input to a “rule” that associates a specific number (the output) with each input. Figure \(\PageIndex \): The function \(31 = f(January)\) where 31 is the output, f is the rule, and January is the input. For example, \(f(\text )=31\), because March has 31 days. The notation \(d=f(m)\) reminds us that the number of days, \(d\) (the output), is dependent on the name of the month, \(m\) (the input).
- Analysis Note that the inputs to a function do not have to be numbers; function inputs can be names of people, labels of geometric objects, or any other element that determines some kind of output.
- However, most of the functions we will work with in this book will have numbers as inputs and outputs.
- Example \(\PageIndex \): Interpreting Function Notation A function \(N=f(y)\) gives the number of police officers, \(N\), in a town in year \(y\).
What does \(f(2005)=300\) represent? Solution When we read \(f(2005)=300\), we see that the input year is 2005. The value for the output, the number of police officers \((N)\), is 300. Remember, \(N=f(y)\). The statement \(f(2005)=300\) tells us that in the year 2005 there were 300 police officers in the town.
- Exercise \(\PageIndex \) Use function notation to express the weight of a pig in pounds as a function of its age in days \(d\).
- Answer \(w=f(d)\) Q&A Instead of a notation such as \(y=f(x)\), could we use the same symbol for the output as for the function, such as \(y=y(x)\), meaning “\(y\) is a function of \(x\)?” Yes, this is often done, especially in applied subjects that use higher math, such as physics and engineering.
However, in exploring math itself we like to maintain a distinction between a function such as \(f\), which is a rule or procedure, and the output y we get by applying \(f\) to a particular input \(x\), This is why we usually use notation such as \(y=f(x),P=W(d)\), and so on.
How do you write a function on a graph?
Given a graph of a line, we can write a linear function in the form y=mx+b by identifying the slope (m) and y-intercept (b) in the graph. GIven a graph of an exponential curve, we can write an exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph.
What is not a function in a graph?
If you can draw a vertical line any where in the graph and it crosses more than 1 point on the graph, then the graph is not a function.
How do you identify functions and non functions?
A function is a relation between domain and range such that each value in the domain corresponds to only one value in the range. Relations that are not functions violate this definition. They feature at least one value in the domain that corresponds to two or more values in the range.
How do you know if it’s a function without graphing?
Example Problem 2: Determining Whether an Equation Defines a Function – Determine whether 7x + y^3 = 19 defines y as a function of x, Step 1: Solve the equation for y, if needed. \begin 7x + y^3 & = 19\\ y^3 & = 19 – 7x\\ y &= \sqrt \end Note that we do not need a \pm symbol when taking a cube root of both sides of the equation.
Is a function just a straight line?
Linear Functions The linear function is popular in economics. It is attractive because it is simple and easy to handle mathematically. It has many important applications. Linear functions are those whose graph is a straight line. A linear function has the following form y = f(x) = a + bx A linear function has one independent variable and one dependent variable.
- To graph a linear function:
- 1. Find 2 points which satisfy the equation
- 2. Plot them
- 3. Connect the points with a straight line
- y = 25 + 5x
- let x = 1 then
- y = 25 + 5(1) = 30
- let x = 3 then
- y = 25 + 5(3) = 40
A simple example of a linear equation A company has fixed costs of $7,000 for plant and equuipment and variable costs of $600 for each unit of output. What is total cost at varying levels of output? let x = units of output let C = total cost C = fixed cost plus variable cost = 7,000 + 600 x
|15 units||C = 7,000 + 15(600) = 16,000|
|30 units||C = 7,000 + 30(600) = 25,000|
Combinations of linear equations
- Linear equations can be added together, multiplied or divided.
- A simple example of addition of linear equations
- C(x) is a cost function
C(x) = fixed cost + variable cost R(x) is a revenue function R(x) = selling price (number of items sold) profit equals revenue less cost P(x) is a profit function P(x) = R(x) – C(x) x = the number of items produced and sold Data: A company receives $45 for each unit of output sold.
|R(x) = 45x||C(x) = 1600 + 25x|
|P(x) = 45x -(1600 + 25x)|
|= 20x – 1600|
Is a function always a line?
No, every straight line is not a graph of a function. Nearly all linear equations are functions because they pass the vertical line test. #y=100# #y=x# #y=4x# #y=10x+4# #y=-2x-9# The exceptions are relations that fail the vertical line test. x = some constant #x = 0# #x=99# #x=-3#
Is a vertical line always a function?
Vertical Line Test – Vertical line test is used to assess whether a given graph represents a function or not. It is based on the fact that a function can only have one output for every input. This test ensures that for each input (x-value), there is only one corresponding output (y-value), satisfying the criteria of a function.
What makes a function a function?
Functions and linear equations (Algebra 2, How to graph functions and linear equations) – Mathplanet
- If we in the following equation y=x+7 assigns a value to x, the equation will give us a value for y.
- $$if\; x=2\; then$$
If we would have assigned a different value for x, the equation would have given us another value for y. We could instead have assigned a value for y and solved the equation to find the matching value of x. In our equation y=x+7, we have two variables, x and y.
The variable which we assign the value we call the independent variable, and the other variable is the dependent variable, since it value depends on the independent variable. In our example above, x is the independent variable and y is the dependent variable. A function is an equation that has only one answer for y for every x.
A function assigns exactly one output to each input of a specified type. It is common to name a function either f(x) or g(x) instead of y. f(2) means that we should find the value of our function when x equals 2.
- $$if\; x=2\; then$$
- A function is linear if it can be defined by
f(x) is the value of the function. m is the slope of the line. b is the value of the function when x equals zero or the y-coordinate of the point where the line crosses the y-axis in the coordinate plane. x is the value of the x-coordinate. This form is called the slope-intercept form.
- The slope, m, is here 1 and our b (y-intercept) is 7. The slope of a line passing through points (x1,y1) and (x2,y2) is given by
- $$m=\frac -y_ } -x_ }$$
- $$x_ \neq x_ $$
- If two linear equations are given the same slope it means that they are parallel and if the product of two slopes m1*m2=-1 the two linear equations are said to be perpendicular.
What makes it not a function?
Answer and Explanation: 1 – Become a Study.com member to unlock this answer! Create your account View this answer We call a relation a function when no two ordered pairs in the relation have the same first coordinate with different second coordinates. The term. See full answer below.
Is a circle on a graph a function?
What is a relation? – There are many naturally occurring formulas whose graphs are not the graphs of functions. For example: The first graph is a circle, the second is an ellipse, the third is two straight lines, and the fourth is a hyperbola. In each example, there are values of \(x\) for which there are two values of \(y\). So these are not graphs of functions. It turns out that the most useful concept to help describe and understand this issue is very general.
What is a function example?
What is a Function in Algebra? – A function is an equation for which any x that can be put into the equation will produce exactly one output such as y out of the equation. It is represented as y = f(x), where x is an independent variable and y is a dependent variable. For example:
y = 2x + 1y = 3x – 2y = 4yy = 5/x
What are the rules for functions?
The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value. A function is written as, where is the input value. The general form of a function is A vertical test is done graphically to determine whether the relation is a function or not.
A vertical line is drawn anywhere on the function. If it intersects the function only at one point, it is a function. If the line intersects at more than one point, it is not a function. –
How do you explain functions in math?
A function is a rule which maps a number to another unique number. In other words, if we start off with an input, and we apply the function, we get an output. For example, we might have a function that added 3 to any number. So if we apply this function to the number 2, we get the number 5.
What is an example of a function?
Types of Functions in Maths – An example of a simple function is f(x) = x 2, In this function, the function f(x) takes the value of “x” and then squares it. For instance, if x = 3, then f(3) = 9. A few more examples of functions are: f(x) = sin x, f(x) = x 2 + 3, f(x) = 1/x, f(x) = 2x + 3, etc. There are several types of functions in maths. Some important types are:
- Injective function or One to one function: When there is mapping for a range for each domain between two sets.
- Surjective functions or Onto function: When there is more than one element mapped from domain to range.
- Polynomial function: The function which consists of polynomials.
- Inverse Functions: The function which can invert another function.
These were a few examples of functions. It should be noted that there are various other functions like into function, algebraic functions, etc. Learn here all the functions: