What do you do to test for a function
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What do you do to test for a function

[From: ] [author: ] [Date: 11-06-19] [Hit: ]
x + y = 4 is a line, meaning it is a linear function.xy = 4 is also a line, meaning it is also a linear function.x^2 + 4x + y = 4 is a vertical parabola, meaning it is a geometric function.......
Which is not a function?

(x - 2)^2 + y^2 = 4

x^2 + 4x + y = 4

x + y = 4

xy = 4

Do you use the Horizontal line rule, or the vertical line rule?

When is the appropriate time to use each test?

BEST ANSWER CHOSEN ASAP!

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Vertical line. If you at any point you can draw a vertical line that crosses the graph twice, it is not a function.

x + y = 4 is a line, meaning it is a linear function.
xy = 4 is also a line, meaning it is also a linear function.
x^2 + 4x + y = 4 is a vertical parabola, meaning it is a geometric function.
(x - 2)^2 + y^2 = 4 is a circle, meaning it is not a function.

The easy way to tell: the y in the last equation has an exponent. If the y has an exponent it's either a circle or a horizontal parabola, which means it fails the vertical line test, and is therefore not a function.

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We use verticle line test
(i) (x - 2)^2 + y^2 = 4 it is a circle which is cut twice by verticle line, therefore not a fuction
(ii) x^2 + 4x + y = 4 this is a parabola opening up and a vertcle line will cut once, it is a function
(iii) x + y = 4 it is a straight line whice is cut once by verticle line, therefore it is a function
(iv) xy = 4 for one valu of x there is one value of y, therefore is also function

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You can restrict the range, (x-2)² + y² = 4 is not a function, but y = √{4 -(x-2)²} is, because we ignore the ±y we get from our square root and only use the positive case. So, the first one is not a function.

Use the vertical line test. The horizontal test to see if the inverse of that function is a function.

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You use the vertical line rule. (x - 2)^2 + y^2 = 4 is not a function.
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