Table of Contents
Can two different functions have the same domain and range?
Hence, every given domain value has one and only one range value as a result, but not necessarily vice versa. In other words, two different values of x can have the same y -value, but each y -value must be joined with a distinct x -value.
Can you have the same domain and range?
Can a function’s domain and range be the same? Yes. For example, the domain and range of the cube root function are both the set of all real numbers.
Can functions have the same domain?
Two functions are equal if they have the same domain and codomain and their values are the same for all elements of the domain.
Which function has the same domain and range?
The function f(x)=ax,a≠0 has the same domain, range and asymptotes as f(x)=1x .
Can the same function be represented by different formulas?
But as you note, if two different formulas for the right hand side actually give the same values when you substitute values from the domain, then the functions so defined will be the same. (,) is a binary operation on functions; it’s defining property is (g,h)(x)=(g(x),h(x)).
Can two functions have the same output?
This relation is a function. Remember that in a function, the input value must have one and only one value for the output. There is a name for the set of input values and another name for the set of output values for a function. The set of input values is called the domain of the function.
Can domain and range have the same number of elements?
If there is to be exactly one present for each friend, there have to be as many presents as friends: the domain has to contain the same number of elements as the range. Conversely, if the domain and range contain the same number of elements, then you can be sure that there is a bijection.
How do you write the domain and range of a function?
The domain and range of a function is the set of all possible inputs and outputs of a function respectively. The domain and range of a function y = f(x) is given as domain= {x ,x∈R }, range= {f(x), x∈Domain}. The domain and range of any function can be found algebraically or graphically.
Does the domain depend on the range?
The domain of a function or relation is the set of all possible independent values the relation can take. It is the collection of all possible inputs. The range of a function or relation is the set of all possible dependent values the relation can produce from the domain values.
How can two functions be the same?
The set A is called the domain of f and the set B is called the codomain. We say two functions f and g are equal if they have the same domain and the same codomain, and if for every a in the domain, f(a)=g(a). We often write f:A→B to indicate that f is a function from A to B.
What makes a function an even function?
DEFINITION. A function f is even if the graph of f is symmetric with respect to the y-axis. Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f.
How do you find the domain and range of a relation?
Remember that ordered pairs are written as (x, y). When looking at a set of ordered pairs, find the domain by listing all the x values from the relation. Find the range by listing all the y values from the ordered pairs.
What is the fundamental difference between a relation and function is every relation a function?
The difference between a relation and a function is that a relationship can have many outputs for a single input, but a function has a single input for a single output. This is the basic factor to differentiate between relation and function. Relations are used, so those model concepts are formed.
What is the difference between domain and range?
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. They may also have been called the input and output of the function.).
Is y a repeating function?
A function is a relation in which the members of the domain (x-values) DO NOT repeat. So, for every x-value there is only one y-value that corresponds to it. y-values can be repeated.
What are four different ways of representing functions?
Key Points A function can be represented verbally. For example, the circumference of a square is four times one of its sides. A function can be represented algebraically. For example, 3x+6 3 x + 6 . A function can be represented numerically. A function can be represented graphically.
Are all functions are relations but not all relations are functions?
All functions are relations, but not all relations are functions. A function is a relation that for each input, there is only one output. Here are mappings of functions. The domain is the input or the x-value, and the range is the output, or the y-value.
Can there be more than one input in a function?
Short answer: Yes. Long answer: Yes, but using the Cartesian product, you can consider multiple inputs as being a single input, where the single input is an ordered pair.
How do you determine whether a function is an inverse of another function?
Let f be a function. If any horizontal line intersects the graph of f more than once, then f does not have an inverse. If no horizontal line intersects the graph of f more than once, then f does have an inverse. The property of having an inverse is very important in mathematics, and it has a name.
Can domain be smaller than range?
Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. Keep in mind that if the graph continues beyond the portion of the graph we can see, the domain and range may be greater than the visible values.
