Combining Functions

MCC9-12.F.BF.1b Combine standard

function types using arithmetic operations.

Adding Linear Functions

f(x) + g(x) If f(x)= 3x - 4 and g(x) = -2x + 6, find f(x) + g(x).(3x – 4) + (-2x + 6)

OR 3x – 4

+ -2x +6 1x + 2So, f(x) + g(x) = 1x + 2

Adding Linear Functions

If f(x) = 7x + 3 and g(x) = 6x – 4, find f(x) + g(x).

Subtracting Linear Functionsf(x) - g(x)

If f(x) = 4x -29 and g(x)= 2x – 18, find f(x) – g(x).(4x – 29) – (2x -18) change – to + the opposite.(4x – 29) + (-2x +18) 4x – 29

+ -2x + 18 2x - 11

So, f(x) – g(x) = 2x – 11

Subtracting Linear Functions

If f(x) = -3x + 15 and g(x) = -4x -17, find f(x) – g(x).

Multiplying Linear Functions

f(x) · g(x) If f(x) = 3x and g(x) = 2x -17, find f(x)·g(x).(3x)(2x-17) = 3x(2x) – 3x(17) = 6x2 – 51So, f(x) · g(x) = 6x2 – 51

Multiplying Linear Functions

If f(x) = x - 13 and g(x) = -5x, find f(x)·g(x).

Dividing Linear Functions

f(x) / g(x)If f(x) = 6x and g(x) = 2x, find f(x)/g(x).6x/2x = 3So, f(x) / g(x) = 3

Dividing Linear Functions

If f(x) = x + 5 and g(x) = 2x, find f(x)/g(x).

Adding exponential functions

f(x) + g(x)If f(x) = 2x and g(x) = 2x, find f(x) + g(x).2x + 2x = 2(2x)

Adding exponential functions

If f(x) = 2(4x) and g(x) = 4x, find f(x) + g(x)

Subtracting exponential functions

f(x) – g(x)If f(x) = 5(8x) and g(x) = 2(8x), find f(x) – g(x).5(8x) – 2(8x) = 3(8x)So f(x) – g(x) = 3(8x)

Subtracting exponential functions

If f(x) = 4(6x) and g(x) = 7(6x), find f(x) – g(x).

Multiplying exponential functions

If f(x) = 52x and g(x) = 5x, then find f(x)·g(x).52x · 5x = 52x + x = 53x When multiplying exponential functions, bases must be the same. You add the exponents.So f(x) · g(x) = 53x

Multiplying exponential functions

If f(x) = 8(9)x and g(x) = 1/2(9)-2x, find f(x) · g(x).

Dividing Exponential Functions

f(x)/g(x)If f(x) = 8(26x) and g(x) = 4(23x), find f(x)/g(x).8(26x)

= 2(23x)

4(23x)

Dividing Exponential Functions

If f(x) = 8(94x) and g(x) = 2(9-3x), find f(x)/g(x).