Answer:
[tex]y=-|x-3|-3[/tex]
Step-by-step explanation:
The table shows values of [tex]y[/tex] for different values of [tex]x[/tex].
Let us test each equation with the values given in the table.
Equation 1: [tex]y=|x+3|-3[/tex]
For [tex]x[/tex] = 1, we get,
[tex]y=|x+3|-3=|1+3|-3=|4|-3=4-3=1[/tex]
So, we got 1 for [tex]y[/tex]. But as per table, value of [tex]y[/tex] should be -5.
So, equation 1 is incorrect.
Equation 2: [tex]y=-|x-3|-3[/tex]
For [tex]x[/tex] = 1, we get,
[tex]y=-|x-3|-3=-|1-3|-3=-|-2|-3=-(2)-3=-5[/tex]
So, we got -5 for [tex]y[/tex]. It matches with the value of table.
Let us check for another value of [tex]x[/tex] in order to confirm.
For [tex]x =2[/tex], we get,
[tex]y=-|x-3|-3=-|2-3|-3=-|-1|-3=-(1)-3=-4[/tex]
So, we got -4 for [tex]y[/tex]. 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: [tex]y=|x-3|-3[/tex]
For [tex]x[/tex] = 1, we get,
[tex]y=|x-3|-3=|1-3|-3=|-2|-3=2-3=-1[/tex]
So, we got -1 for [tex]y[/tex]. But as per table, value of [tex]y[/tex] should be -5.
So, equation 3 is incorrect.
Equation 4: [tex]y=-|x+3|-3[/tex]
For [tex]x[/tex] = 1, we get,
[tex]y=-|x+3|-3=-|1+3|-3=-|4|-3=-4-3=-7[/tex]
So, we got -7 for [tex]y[/tex]. But as per table, value of [tex]y[/tex] should be -5.
So, equation 4 is incorrect.
