Question

1. which of the following equations could represent the relationship between x and y in the table below?

y	x
3	1
9	2
19	3
33	4

y = 3x
y = 2x^{2}+1
y=\frac{3}{x}
y = x^{2}+2

Explanation:

Step1: Test first option $y = 3x$

When $x = 1$, $y=3\times1 = 3$; when $x = 2$, $y = 3\times2=6
eq9$. So this is not the correct equation.

Step2: Test second option $y = 2x^{2}+1$

When $x = 1$, $y=2\times1^{2}+1=2 + 1=3$; when $x = 2$, $y=2\times2^{2}+1=2\times4 + 1=9$; when $x = 3$, $y=2\times3^{2}+1=2\times9+1 = 19$; when $x = 4$, $y=2\times4^{2}+1=2\times16 + 1=33$. This equation satisfies all the pairs in the table.

Step3: Test third option $y=\frac{3}{x}$

When $x = 1$, $y = 3$; when $x = 2$, $y=\frac{3}{2}
eq9$. So this is not the correct equation.

Step4: Test fourth option $y=x^{2}+2$

When $x = 1$, $y=1^{2}+2=3$; when $x = 2$, $y=2^{2}+2=6
eq9$. So this is not the correct equation.

Answer:

$y = 2x^{2}+1$