Identify Functions
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Question 1 of 7
1. Question
Identify if the curve x=y2 is a function- 1.
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There are two ways to check if an equation is a function: the algebraic method and the vertical line testMethod One: Algebraic MethodSubstitute any value to x and solve for y. A function should have one value for y for every value of xx = y2 2 = y2 Substitute x=2 √2 = √y2 Find the square root of both sides √2 = y y = ±√2 y has 2 values (√2,-√2) for one value of x (2). Therefore, the equation is not a functionNot a FunctionMethod Two: Vertical Line TestDraw a vertical line at any point of the curve. If the line intercepts the curve more than once, it is not a function.At x=2, the vertical line intercepts the curve line twice. Therefore, x=y2 is not a functionNot a Function -
Question 2 of 7
2. Question
Identify if the curve y=2x is a function-
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The vertical line test is a method to check if a curve in a graph is a function by using a vertical lineDraw a vertical line at any point of the curve. If the line intercepts the curve more than once, it is not a function.The vertical line intercepts the curve line once. Therefore, y=2x is a functionFunction -
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Question 3 of 7
3. Question
Identify if the curve x2+y2=9 is a function-
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The vertical line test is a method to check if a curve in a graph is a function by using a vertical lineDraw a vertical line at any point of the curve. If the line intercepts the curve more than once, it is not a function.The vertical line intercepts the curve line twice. Therefore, x2+y2=9 is not a functionNot a Function -
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Question 4 of 7
4. Question
Identify if the curve y=√4-x2 is a function-
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The vertical line test is a method to check if a curve in a graph is a function by using a vertical lineDraw a vertical line at any point of the curve. If the line intercepts the curve more than once, it is not a function.The vertical line intercepts the curve line once. Therefore, y=√4-x2 is a functionFunction -
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Question 5 of 7
5. Question
Identify if the curve is a function-
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The vertical line test is a method to check if a curve in a graph is a function by using a vertical lineDraw a vertical line at any point of the curve. If the line intercepts the curve more than once, it is not a function.The vertical line intercepts the curve line once. Therefore, the curve is a functionFunction -
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Question 6 of 7
6. Question
Identify if the curve is a function-
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The vertical line test is a method to check if a curve in a graph is a function by using a vertical lineDraw a vertical line at any point of the curve. If the line intercepts the curve more than once, it is not a function.Notice that if the vertical line is drawn at this point, it intercepts both the empty circle (“less than/greater than” indicator) and the filled circle (“less than or equal/greater than or equal” indicator)The empty circle is not included to the value of the curve, so the vertical line intercepts the curve only once. Therefore, it is a functionFunction -
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Question 7 of 7
7. Question
Identify if the line is a function-
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The vertical line test is a method to check if a curve in a graph is a function by using a vertical lineSince the curve itself is a vertical line, the value of x (3) has all real values of yThe x value should only have one y value for it to be a function. Therefore, the curve is not a functionNot a Function -
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