Determining If an Equation Is a Function

A method of testing whether a graph represents a function by determining whether a vertical line intersects the graph of no more than once.

• Vertical Line Test

• Horizontal Line Test

• T Test

• Z Test

Grace is analyzing a relationship between two variables in her math class. She comes across the equation y - 1/x = 11. Determine whether this function is linear or nonlinear.

• Linear

• Nonlinear

Answer explanation

The function y - 1/x = 11 is nonlinear because it contains a term with x in the denominator, making it non-linear.

Is the equation a function?

• Yes - the y variable has an odd exponent (1)

• No - the x variable is squared

• No - the y-intercept is negative

• No - a function has to be in the form of y=mx + b

Does the equation y=3x-5 represent a function?

• Yes

• No

• No idea

How can you determine if a given equation represents a function?

• Use the vertical line test

• Check if the equation has more than one solution

• Use the horizontal line test

• Count the number of variables in the equation

IS THIS EQUATION A FUNCTION? (CLUE: PLUG IN 2 FOR X AND SEE IF YOU GET THE SAME ANSWER EACH TIME)

• YES

• NO

Is the following equation considered a function? y=-x²-4x

• yes 

• no

Does the equation y=x represent a function? Why or why not?

• No, it is a proportional relationship and that would not pass the vertical line test if graphed.

• No, the equation y = x has two variables so it could not be graphed, plotted or put in a table.

• Yes. it is a proportional relationship with a positive slope so it would pass the vertical line test.

• Yes, the equation has a negative slope and a positive y-intercept so the equation would be a function.

• Yes, it defines y as a function of x.

• No, it does not define y as a function of x.

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