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Checking if an equation represents a function

Sal determines if y is a function of x from looking at an equation. Created by Sal Khan.

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• Is it safe to say that if there are exponents in the relationship that it will not be a function? Is this generally true? Thanks
• Not necessarily.

Take the relationship y = x^2
y can be a function of x because every x value has only one y value.
But x could not be a function of y, because each positive y has two x values.
• but how did he make that arc? How will you know what shape to draw on a line?
• Not sure yet dude, but one thing I've found on Khan Academy is to trust Sal and then later on you find the answers down the track. I've found that when he introduces concepts you don't understand, generally it seems you don't need to understand how to do them at this stage (if you are following through a logical progression). Looking at an equation and being able to draw it is probably something that comes from a ton of experience!
• At , how does Sal just know that y=square root of (x-3) gives off that curved line. Similarly, with the negative version... It's not even in proper slope-intercept form so how the heck does he know where the hell the line is going. Someone please help!
• I really don't understand any of this!
• Couldn't I just plug this equation into my graphing calculator since they are allowed in most high school math classes and the math sats?
• That depends on whether you understand the concepts. It is fine to have software to help you get through the tedious computations, but if you do not understand how to do the graph yourself, your calculator won't be much help.

• this example is a bit more confusing than the others…😵‍💫
• So from what I understand a functions can't be any value that's taken to an even power (but the rules and inputs can be). What other mathematical concepts are there that prevent a relation from being a function?
(1 vote)
• At
How do you suppose "y=square root of (x-3)" or the negative version gives you that curved line? That literally makes zero sense to me. He doesn't even have it in slope-intercept form to do that. Someone please explain!
• Squaring a number will always give you the same output `(-3)^2 = 9 = 3^2`
Taking the square root of a number could result in a positive or negative output `√9 = ±3`