# Subtracting functions

### Subtracting functions

#### Lessons

subtracting functions: $(f-g)(x) = f(x)-g(x)$
• 1.
Determine the Difference of Two Functions Algebraically
If $f(x)= 5x^3-x+6$
and
$g(x)=4x-8,$
Determine:
a)
$(f-g)(x)$

b)
$(g-f)(x)$

c)
$(g-f)(-2)$
evaluate in two different ways

• 2.
Determine the Difference of Two Functions Graphically
Given the graphs of functions $f(x)$
and $g(x)$

a)
sketch: $(g-f)(x)$

b)
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 $y=(f-g)(x)?$
a)
$(0,-1)$

b)
$(0,1)$

c)
$(2,-1)$

d)
$(3,30)$