# Dividing functions

### Dividing functions

#### Lessons

Dividing functions: $(\frac{f}{g})(x)=\frac{f(x)}{g(x)}$
• 1.
Determine the Quotient of Two Functions and State Its Domain
Write an expression in the simplest form for $(\frac{f}{g})(x)$
State the domain restrictions
a)
$f(x)=3x-8$
$g(x)=x+2$

b)
$f(x)=4x^3+5x^2$
$g(x)=x$

c)
$f(x)=2x^2+4x-30$
$g(x)=2x-6$

d)
$f(x)=x-3$
$g(x)=x^2+2x-15$

• 2.
Operations of Functions – In a Nutshell
Consider the functions $f(x)=\frac{x}{x+5}$
and $g(x)=\frac{3x}{x-2}$
a)
state the domain of $f(x)$
and $g(x)$

b)
write an expression in the simplest form for each
of the following and state the domains
i) $(f+g)(x)$
ii) $(f-g)(x)$
iii) $(fg)(x)$
iv) $(\frac{f}{g})(x)$

c)
evaluate $(\frac{f}{g})(4)$
in 2 different ways

• 3.
Sketch the Quotient of Two Functions
Consider the functions $f(x)=2x^2+4x-30$
$g(x)=20x-60$
a)
Determine the equation of the function
$h(x)=(\frac{g}{f})(x)$ and state the domain restrictions

b)
Sketch the graph of
$h(x)=(\frac{g}{f})(x)$