Question

Which equation best represents the relationship shown in the following ordered pairs?(-4, 16), (-2, 4), (0, 0),(1,1) A. y = x^2B. y = -4xC. y = xD. y = -2x + 8

Answer 1

from the given information, we have:

f(-4) = 16

f(-2) = 4

f(0) = 0

f(1) = 1

we need to find an equation that represents the above.

Let's try option A

`\begin{gathered} f(-4)=(-4)^2=16 \\ f(-2)=(-2)^2=4 \\ f(0)=(0)^2=0 \\ f(1)=(1)^2=1 \end{gathered}`

we can see that the equation y=x^2 represents all ordered pairs

On the other hand, option B will be:

`\begin{gathered} f(-4)=-4\cdot(-4)=16 \\ f(-2)=-4\cdot(-2)=8 \\ f(0)=-4\cdot(0)=0 \\ f(1)=-4\cdot(1)=-4 \end{gathered}`

We can see that option B does not represent all ordered pairs

Now, let's explore option C:

`\begin{gathered} f(-4)=-4 \\ f(-2)=-2 \\ f(0)=0 \\ f(1)=1 \end{gathered}`

again, as in option B, option C does not represent all ordered pairs

finally, let's explore option D, just to make sure:

`\begin{gathered} f(-4)=-2\cdot(-4)+8=16 \\ f(-2)=-2\cdot(-2)+8=12 \\ f(0)=-2\cdot(0)+8=8 \\ f(1)=-2\cdot(1)+8=6 \end{gathered}`

again, as in options B and C, option D also does not represent all ordered pairs

in conclusion, option A is the one that best represents the relationship