Subject Math

Have you observed a pattern? If yes, state so.

a. f(x) = 2x (increases)

b. f(x) = 2x + 1 (increases)

c. f(x) = -3x (decreases)

d. f(x) = -3x – 4 (decreases)

e. f(x) = 2 – 3x (decreases)

answer

Yes, I have observed a pattern. From the given values of x, substituting the numbers to each function will prove and support the answer to be stated. There are different functions to substitute the 3 values for each functions and pattern can be observed from that point. Determining the values as (a) f(-3), (b) f(1), and (c) f(4) in each of the following functions, the values of f(x) as x increases would be:

a. f(x) = 2xLet x= -3, f(-3) = 2(-3) , therefore ,the value of f(x) at x =-3 is -6.Let x=1, f(1) = 2(1) , therefore ,the value of f(x) at x = 1 is 2Let x=4, f(4) = 2(4) , therefore ,the value of f(x) at x = 4 is 8.

Pattern Observed

The value of f(x) in the function f(x) = 2x increases as x increases in a positive function.

b. f(x) = 2x + 1Let x= -3, f(-3) = 2(-3) + 1 , therefore ,the value of f(x) at x = -3 is -5.Let x=1, f(1) = 2(1) + 1 , therefore ,the value of f(x) at x = 1 is 3.Let x=4, f(4) = 2(4) + 1, therefore ,the value of f(x) at x = 4 is 9.

Pattern Observed

The value of f(x) in the function f(x) = 2x + 1 increases as x increases in a positive function.

c. f(x) = -3xLet x= -3, f(-3) = -3(-3) , therefore ,the value of f(x) at x = -3 is 9.Let x=1, f(1) = -3(1), therefore ,the value of f(x) at x = 1 is -3.Let x=4, f(4) = -3(4), therefore ,the value of f(x) at x = 4 is -12.

Pattern Observed

The value of f(x) in the function f(x) = -3x decreases as x increases in a negative function.

d. f(x) = -3x – 4Let x= -3, f(-3) = -3(-3) -4 , therefore ,the value of f(x) at x = -3 is 5.Let x=1, f(1) = -3(1) - 4, therefore ,the value of f(x) at x = 1 is -7.Let x=4, f(4) = -3(4) -4 , therefore ,the value of f(x) at x = 4 is -16.

Pattern Observed

The value of f(x) in the function f(x) = -3x - 4 decreases as x increases in a negative function.

e. f(x) = 2 – 3xLet x= -3, f(-3) =2-3(-3), therefore ,the value of f(x) at x = -3 is 11.Let x=1, f(1) = 2-3(1), therefore ,the value of f(x) at x = 1 is -1.Let x=4, f(4) = 2-3(4) , therefore ,the value of f(x) at x = 4 is -9.

Pattern Observed

The value of f(x) in the function f(x) = 2 -3x decreases as x increases in a negative function.

Code 8.3.2.3.3