9) x y
0 0
1 3
2 12
3 27
a.What type of function is this?
b.What is the value of x=5?
a.) as x increases by one, you multiply by the next multiple of 3 to get y. 1x3=3, 2x6=12, 3x9=27, etc.
b.) if x=5 then y=75
f(1) = 3 = 1x3
f(2) = 12 = 2x6
f(3) = 3x9
f(x) = x(3x) = 3x^2 ---> quadratic function
f(5) = 3(25) = 75
notice f(0) = 3(0^2) = 0 also fits
To determine the type of function from the given values, we can observe how the values of y correspond to the values of x.
Looking at the given values, we see that as x increases by 1, y increases by the cube of x. For example, when x = 0, y = 0^3 = 0. When x = 1, y = 1^3 = 1. When x = 2, y = 2^3 = 8. When x = 3, y = 3^3 = 27.
Since the values of y are equal to the cube of x, we can conclude that the function is a cubic function.
To find the value of y when x = 5, we can use the same pattern. When x = 5, y would be equal to 5^3 = 125.
So, the value of y when x = 5 is 125.