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3 years ago

Use algebraic means to show that x^2 + y^2 = 8 is not a function. Explain your process.

Mathematics

1 answer:

11Alexandr11 [23.1K]3 years ago

5 0

Answer:

For a single value of x function has more than one corresponding value of y which satisfies the equation.

Step-by-step explanation:

Function: A relationship between a set of inputs and a set of possible outputs, where exactly one output is associated with each input.

It means for an equation to represent a function any single value of x there should be only one corresponding value of y which satisfies the equation.

Now consider the given equation.

$x^2 + y^2 = 8$

If we put x=0 then we get two value of y i.e $\sqrt8$ and $-\sqrt8$ which satisfy the equation and therefore the equation is not a function.

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Check the picture below.

$\bf 0=AB^2+6AB-121\implies \stackrel{\textit{using the quadratic formula}}{AB=\cfrac{-6 \pm \sqrt{6^2-4(1)(-121)}}{2(1)}}
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