Question

Which equation is represented by the table?

Answer 1

Answer:

$y=-|x-3|-3$

Step-by-step explanation:

The table shows values of $y$ for different values of $x$.

Let us test each equation with the values given in the table.

Equation 1: $y=|x+3|-3$

For $x$ = 1, we get,

$y=|x+3|-3=|1+3|-3=|4|-3=4-3=1$

So, we got 1 for $y$. But as per table, value of $y$ should be -5.

So, equation 1 is incorrect.

Equation 2: $y=-|x-3|-3$

For $x$ = 1, we get,

$y=-|x-3|-3=-|1-3|-3=-|-2|-3=-(2)-3=-5$

So, we got -5 for $y$. It matches with the value of table.

Let us check for another value of $x$ in order to confirm.

For $x =2$, we get,

$y=-|x-3|-3=-|2-3|-3=-|-1|-3=-(1)-3=-4$

So, we got -4 for $y$. It matches with the value of table.

So, equation 2 is the correct answer.

We can be completely sure by checking the remaining equations too.

Equation 3: $y=|x-3|-3$

For $x$ = 1, we get,

$y=|x-3|-3=|1-3|-3=|-2|-3=2-3=-1$

So, we got -1 for $y$. But as per table, value of $y$ should be -5.

So, equation 3 is incorrect.

Equation 4: $y=-|x+3|-3$

For $x$ = 1, we get,

$y=-|x+3|-3=-|1+3|-3=-|4|-3=-4-3=-7$

So, we got -7 for $y$. But as per table, value of $y$ should be -5.

So, equation 4 is incorrect.