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### Course: Get ready for Algebra 2>Unit 3

Lesson 4: Recognizing functions

# Recognizing functions from graph

Checking whether a given set of points can represent a function. For the set to represent a function, each domain element must have one corresponding range element at most. Created by Sal Khan and Monterey Institute for Technology and Education.

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• heres another example: if a class is taking a test, the students would be the domain and the grades would be the range. one student cannot get more than one grade, just like how one domain can have only one range. however, more than one students can get the same grade, like how there can be multiple domains for a range.
• well, if they have students with the same range, than why did anyone not notice that we have different domains? I'll let someone else think about that.
• Does this mean f(x) = sqrt of x is not a function? It has two outputs; for example if we input 9 in we get -3 or positive 3.
• f(x)=sqrt(x) is a function. If you input 9, you will get only 3. Remember, sqrt(x) tells you to use the principal root, which is the positive root. If the problem wanted you to use the negative root, it would say "- sqrt(x)".
• At , Sal writes the function as -1-->f-->3. Can you write the same function as f(-1)= 3?
• I think so, because then why do we have a negative one?
(1 vote)
• I know a regular parabola is a function as it passes the vertical line test, but what about the horizontal line test, you can have multiple inputs for a given output, for example you can have 2x values for one y value (as Y is the dependent output). Is my logic correct? Thanks
• It's only the vertical line test that disqualifies it from being a function. There's a lot of functions that don't pass the horizontal line test. For example, the basic functions in trigonometry form waves, which wiggle back and forth forever. If you draw a horizontal line through it, it will intersect infinitely many points on that function.
• So technically, you're just saying that if you enter... let's say...the variable "x" into the x(y) box, and you get y, it's a function. If you get more than one variable from the x(y) box, then it's not a function, right?
• that's correct
• What exactly is a relation and what is the difference between relation and a function?
(1 vote)
• A relation is a set of ordered pairs.
A function is a relation where each input value (x-value) has only one output (y-value).
Thus, all functions are relations. But, not all relations are functions because not all will meet the requirement that each unique input creates only one output .

Hope this helps.
• how do you recognize functions from graphs. mind is lost.
• You use the vertical line test. 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. The reason this works is that points on a vertical line share the same x-value (input) and if the vertical line crosses more than one point on the graph, then the same input value has 2 different output values (y-values) on the graph. So, it fails the definition of a function where each input can have only one ouput.
• Why is it not a function? Help!
• If there is an x value that goes to two y values it is not a function. In this case x=4 goes to y=-1 and y=5

Does that make sense?