these questions are for practice, they don't count as points, but i don't understand how to solve them.. can someone please explain them to me??

Question

which function rule represents the data in the table below?

input|1| 2| 3| 4|5
output|9|15|21|27|33

A)y=4+5x
B)y=3+6x
C)y=5+4x
D)y=6+3x

Which function rule represents the data in the table?

x|-3|-2|-1|0|1
y|-1| 2| 5|8|11

A)y=-3x-8
B)y=1/3x-8
C)y=1/3x+8
D)y=3x+8

Which quadratic rule represents the data table?

x|-1|0|1|2|3
y| 6|5|6|9|14

A)y=2x^2+5
B)y=-x^2
C)y=x^2+5
D)y=x^2+5

I don't exactly understand these questions.. @Writeacher or @Mrs. Sue can you help me?

Answer 1

input|1| 2| 3| 4|5
output|9|15|21|27|33
Note that y increases by 6 for each increase of 1 in x. So, your rule will look like

y = 6x
But, using x=1, 6x=6, but y=9. So, we're too low by 3. That means

y = 3+6x

You can easily verify that this rule works for the other entries in the table.

Similarly, for
x|-3|-2|-1|0|1
y|-1| 2| 5|8|11
y grows by 3 for each 1 in x. So, try
y = 3x
But 3(-3) = -9, so that means
y = 3x+8

For the quadratic,
x|-1|0|1|2|3
y| 6|5|6|9|14

Note that f(-1) = f(1). That means the vertex is midway between them, at x=0. Since y(0) = 5, we try

y = (x-0)^2+5 = x^2+5
You can see that that rule works for all the table entries.

Answer 2

Thank you so so much, i understand now :)

Answer 3

which quadratic rule represents the data in the table? x: -1|0|1|2|3| y:-4|-5|-4| -1|4|

I also need help! thanks

Answer 4

which quadratic rule represents the data in the table? x: -1|0|1|2|3|
y:-4|-5|-4| -1|4|

I also need help! thanks