Question

Lucy found that a solution of x = - 4 was extraneous for her function. What would be a possible denominator in Lucy's function?

A) x2 + 3x - 4

B) x2 - 9

C) x + 5

D) x - 4

Answer 1

The answer is A.
`x^2+3x-4`

Explanation:

In order to determine the correct Lucy's function, we need to understand the meaning of solution of the equation.

The solution of a equation is the value of the variable that makes the function gives a zero value.

So, to find the correct function, we replace the value x=-4 in every options. If the function gives zero, so that will be the correct Lucy's function.

Given
`x=-4`

`x^2+3x-4\\(-4)^2+3*(-4)-4\\16-12-4\\0`

`x^2-9\\(-4)^2-9\\16-9\\7`

`x+5\\(-4)+5\\1`

`x-4\\(-4)-4\\-8`

So, the Lucy's function that gives zero value is
`x^2+3x-4`.

Answer 2

The correct answer for the given question above would be option A. The possible denominator in Lucy's function in which she found that a solution of x = -4 was extraneous for her function is that, x2 + 3x - 4. For that case, it is the first one since it is the same as (x+4)(x−1) which cannot have x=−4 as that would make the denominator zero.