Identifying Functions
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Question 1 of 7
1. Question
Identify if the curve `x=y^2` is a function
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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 `x``x` `=` `y^2` `2` `=` `y^2` Substitute `x=2` `sqrt2` `=` `sqrt(y^2)` Find the square root of both sides `sqrt2` `=` `y` `y` `=` `+-sqrt2` `y` has `2` values `(sqrt2, -sqrt2)` for one value of `x (2)`. Therefore, the equation is not a function`\text(Not a Function)`Method 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=y^2` is not a function`\text(Not a Function)` -
Question 2 of 7
2. Question
Identify if the curve `y=2^x` 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=2^x` is a function`\text(Function)` -
Question 3 of 7
3. Question
Identify if the curve `x^2+y^2=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, `x^2+y^2=9` is not a function`\text(Not a Function)` -
Question 4 of 7
4. Question
Identify if the curve `y=sqrt(4-x^2)` is a function
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Correct!
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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=sqrt(4-x^2)` is a function`\text(Function)` -
Question 5 of 7
5. Question
Identify if the curve is a function
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Keep Going!
Incorrect
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 function`\text(Function)` -
Question 6 of 7
6. Question
Identify if the curve is a function
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Fantastic!
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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 function`\text(Function)` -
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 `y`
The `x` value should only have one `y` value for it to be a function. Therefore, the curve is not a function`\text(Not a Function)`