Given the sequence 2, 4, 6, 8, where x = 0, 1, 2,

what is the function rule?

f(x) = 2x + 2

f(x) = 2

f(x) = 2x

f(x) = 2x − 1

The function rule for the given sequence is f(x) = 2x + 2.

Step-by-step explanation:

A function is a relation which implies that for every input, there will be one output. i.e. for every value of x, there is only one value for y. The function rule describes how to convert an input value (x) into an output value (y) for a given function.

In the given function,

                     f(x) = 2x + 2, where x = 0, 1, 2,

substituting x = 0, we get

                     f(x) = 2(0) + 2 = 2

substituting x = 1, we get

                     f(x) = 2(1) + 2 = 4

substituting x = 2, we get

                     f(x) = 2(2) + 2 = 6

and it goes on like 2, 4, 6, 8,

This satisfies the function f(x) = 2x + 2.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.