# Subtracting functions

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##### Examples
###### Lessons
1. Determine the Difference of Two Functions Algebraically
If $f(x)= 5x^3-x+6$
and
$g(x)=4x-8,$
Determine:
1. $(f-g)(x)$
2. $(g-f)(x)$
3. $(g-f)(-2)$
evaluate in two different ways
2. Determine the Difference of Two Functions Graphically
Given the graphs of functions $f(x)$
and $g(x)$

1. sketch: $(g-f)(x)$
2. evaluate:
i)
$(g-f)(-3)$
ii)
$(g-f)(0)$
iii) $(g-f)(4)$
3. Determine the Difference of Two Functions Point-by-Point
The graph of $y=f(x)$
includes the points (2,5),(4,15),(7,30)
The graph of $y=g(x)$
includes the points (2,6),(3,16),(4,30)
If f and g are defined for all real values of x , then which of the
following points must lie on the graph of $y=(f-g)(x)?$
1. $(0,-1)$
2. $(0,1)$
3. $(2,-1)$
4. $(3,30)$
###### Topic Notes
subtracting functions: $(f-g)(x) = f(x)-g(x)$