Question

1. what are the zeros shown on this graph? y = x^3 - x

Explanation:

Step1: Recall zero - definition

The zeros of a function are the x - values for which y = 0. So we set $y=x^{3}-x = 0$.

Step2: Factor the equation

Factor out an x first: $x(x^{2}-1)=0$. Then use the difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$ to factor $x^{2}-1=(x + 1)(x - 1)$. So the factored form is $x(x + 1)(x - 1)=0$.

Step3: Solve for x

Set each factor equal to zero:
If $x=0$, then it is a zero.
If $x + 1=0$, then $x=-1$.
If $x - 1=0$, then $x = 1$.

Answer:

$x=-1,0,1$