Question

Study this table. x y –3 –2 –2 0 0 4 4 12 Which best describes the function represented by the data in the table? linear with a common ratio of 2 linear with a common first difference of 2 quadratic with a common ratio of 2 quadratic with a common first difference of 2

Answer 1

we can do this by 2 ways

1- by plotting the points on graph and then tracing the points to get shape,

for linear, we will get straight line

for quadratic, we will get parabola

in this case, it is linear as we get a straight line

2- by solving for values of x and y

consider standard linear equation y = mx +c where m is slope and c is constant

by putting given values of x and y we get

y + 2x = 4(answer)

if we consider standard parabola equation

y^2 = 4ax

this equation is not true for given points

Answer 2

Answer:

linear with a common first difference of 2

Step-by-step explanation:

If this is linear, the common first difference, or slope, will be the same throughout the entire table.

The formula for slope is

$m=\frac{y_2-y_1}{x_2-x_1}$

For the first set of points, we have:

m=(0--2)/(-2--3) = (0+2)/(-2+3) = 2/1 = 2

For the second set of points, we have:

m = (4-0)/(0--2) = 4/(0+2) = 4/2 = 2

For the third set of points, we have:

m = (12-4)/(4-0) = 8/4 = 2

The rate of change, or slope, is constant; this makes the function a linear function with a common first difference of 2.