This map shows ordered pairs that belong to the function f(x)=x^2. What is the missing value?

Question

X: -2, -1, 0, 1, ___
Y: 0, 1, 4
______

Answer 1

The function given is $f(x)=x^2$. To find the missing value in the x-values and the corresponding y-values for this function, we can calculate $f(x)$ for the x-values provided.

We know:

• When $x=-2$: $f(-2)=(-2{)}^2=4$
• When $x=-1$: $f(-1)=(-1{)}^2=1$
• When $x=0$: $f(0)=0^2=0$
• When $x=1$: $f(1)=1^2=1$

The ordered pairs for these calculations are:

• For $x=-2$, $y=4$ → ordered pair: $(-2,4)$
• For $x=-1$, $y=1$ → ordered pair: $(-1,1)$
• For $x=0$, $y=0$ → ordered pair: $(0,0)$
• For $x=1$, $y=1$ → ordered pair: $(1,1)$

From the values of $y$ listed in your question (0, 1, 4) and the pattern established, we need to find the corresponding $x$ value when $f(x)=4$.

The only missing value of $x$ that will produce $f(x)=4$ is:

• When $x=2$: $f(2)=2^2=4$

Thus, the missing value for $x$ in the list is $2$.

So, the completed lists will be: X: -2, -1, 0, 1, 2 Y: 4, 1, 0, 1, 4