Answer:
Q = { (x,y) : (0,0), (1,2), (2,16), (3, 54), (4, 128), (5,250) } is cubic
R= { (x,y) : (2,3), (4,4), (6,5), (8,6) } is linear
S = { (x,y), : (1,3), (2,9), (3,17), (4,27), (5, 39), (6,53) } is quadratic
Equation of the linear relation is
y = 0.5x + 2
Step-by-step explanation:
A linear equation has the form y = mx + b where m is the slope and b is the y-intercept. Slope is a constant and growth of function is determined by x value
A quadratic equation has the general form y = ax² + bx + c where a b and c are constants. Growth of the function is mostly determined by the square of x
A cubic equation has the general form y = ax³ + bx² + cx + d where a, b and c are constants. The growth of the function is mostly determined by the cube of x value
Looking at the three relations
#1 is obviously cubic since the value of y appears to be determined by the cube of the value of x. Specifically, when x = 0, y = 0/. When x =1, y = 2 but when x =2, y =16 and 16 is 2x³ = 2(2³) = 2 x 8
Looking at x =3, 2(3³) = 2(27) = 54
So this is a cubic function
#2 is obviously a linear function When x increases by 2, y increases by 1 so it is a linear growth
#3 In this equation we can see that the y value appears to be controlled by the square of x. The specific equation is y = x² + 3x -1
For the linear equation, find the slope from the first two points
m = (4-3)/(4-2) = 1/2 = 0.5
So the equation is y = 0.5x + b
To find b, use the coordinates of any point. Let's choose (4,4)
At x = 4, y = 4 so
4 = (0.5)4 + b = 2+b yielding b = 2
So the equation is y = 0.5x + 2
