Question

Explain how to write a function rule from the table below. Then write a function rule.

x 2 4 6
y 1 0 -1

Answer 1

I'm not exactly sure what a "function rule" is. But I can tell you that there are many functions that satisfy these values. A function takes any value in its domain, and assigns it a uniqe value in its codomain.

Answer 2

The question is asking for A function not THE function. So any function that satisfies those values will work.
So,
$$
f(2)=1\\
f(4)=0\\
f(6)=-1
$$
Where \(f(x)\) is the "rule," which we can call a function.
Here is our function
$$
f=\left\{\begin{matrix}
1&\text{ for x = 2} \\
0&\text{ for x = 4} \\
-1&\text{ for x = -1}
\end{matrix}\right.
$$
This is one way to implement this rule.

There can be many other rules that will satisfy the conditions of your table as @richyw indicated.

Answer 3

Does this make sense?

Answer 4

*Correction on function
$$
f=\left\{\begin{matrix}
1&\text{ for x = 2} \\
0&\text{ for x = 4} \\
-1&\text{ for x = }\color{red}{6}
\end{matrix}\right.
$$

Answer 5

in that case the domain of the function would be the set {2,4,6}

Answer 6

That's right!

Answer 7

if you want the domain of the function to be for all real numbers, you could take ybarapp's functiong and write it using inequalities:\[f=\left\{\begin{matrix}
1&x \leq 2 \\
0& 2 < x \leq 4 \\
-1&x > 4
\end{matrix}\right.\]

Answer 8

Note also that \(\large{y=-\cfrac{1}{2}x + 2}\) also satisfies the equation. But this would just be another rule and it's domain would be larger: