Question

2. Which of the following equations define y as a function of x? Justify your answers.
(a) y = x² + x + 1
(b) x = y^2
(c) x + y^3 = 0​

Answer 1

Answer:

part a is correct answer

Step-by-step explanation:

It is relatively easy to determine whether an equation is a function by solving for y. When you are given an equation and a specific value for x, there should only be one corresponding y-value for that x-value. For example, y = x + 1 is a function because y will always be one greater than x.

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Answer 2

(a) $y=x^{2}+x+1$

Option (a) $y=x^{2}+x+1$ defines $y$ as a function of $x$.

Step-by-step explanation:

• When a variable can be expressed as a linear, quadratic or higher order (integral value) formation by another variable, then the first variable is said to be a function of the second variable.

Here, $y=x^{2}+x+1$ is our best choice because all the powers of $x$ are integral.

Option (b) and (c) define $x=f(y)$ and $f(x,y)=0$ respectively.