A function refers to a set of rules, that provide a set of output values for each and every input value from its domain. It relates each element of its domain (input) to exactly one element to its range (output).
A function is mostly represented as it is pronounced as, f of x.
A function could be broadly classified as Injective Function, Surjective Function, and Bijective Function.
It is also called a One-to-One function. It will have a unique output for each input. This does not mean that each output will have some input.
It is also called a Onto Function. It will have at least one input for every output. This means, for the same output, it could have more than one input.
This is also called a One-to-One and Onto function. It will have exactly one output for each and every input.
Question 1: Analyze the following graph, and name the type of function.
Explanation: The given function is discontinuous at , before, and after the point , it has distinct input for distinct output.
However, it has an extra output represented by a white circle. This means it is an Injective Function.
Question 2: Analyze the following graph, and name the type of function.
Explanation: The given function has two inputs for one output . This means it has more than one input for the same output. So, this is a surjective function.
Question 3: Analyze the following graph, and name the type of function.
Explanation: The following function has exactly one output for every input, so it will be a Bijective Function.
Function is a high school math topic that is essential to learn and understand for every student. Wondering Why? Because Function in math is the only way by which we can calculate output based on the relation between various input variables. SAT math syllabus also includes questions on linear functions, quadratic functions, and Algebraic functions.
Functions can be considered as foundational blocks that help us do a lot of day to day operations from helping airplanes fly safely to creation of new machines and much more! Functions are also used by research for predicting natural disasters & by medical scientists for curing diseases.
For high school students, Functions Homework can be very challenging if the concept, definition, and basics are not strong. At school, many times students feel shy and don’t ask their teachers for more examples or details to understand the fundamentals clearly and start to fear the topic or subject completely.
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Question1: How to graph piecewise functions?
A piecewise function is one in which the output is defined by more than one formula. Every formula has its own domain, and the function's domain is the sum of these smaller domains.
To plot the graph of piecewise function
Question2: How to graph rational functions?
For plotting graph of rational functions following steps should be followed:
Question3: How to graph quadratic functions?
The quadratic equation is the function of degree 2. The graph of quadratic function is a parabola.
To plot the graph of quadratic functions following steps should be followed:
And finally, plot the graph.
Question4: How to solve functions?
For solving any function, we must find out the value of x. Now it depends on the type of the equation.
Let's take an example of linear function f(x) = ax+b
Question5: How to graph log functions?
For log function, characteristics of log must be followed:
To plot the graph
Finally, state the domain, (0,∞), the range, (−∞,∞), and the vertical asymptote, x =0.