AP Calculus AB
Worksheet – Functions, Domain, Range, Piecewise
Name __________________________________
Given the function f ( x)  3x2  2 x , evaluate each function at the requested value.
f (  3) 
f (2) 
 1
f 
t
f (3t 2 ) 
f (a  1) 
f (c  h)  f (c)

h
State the natural domain of the given functions.
f ( x) 
f ( x) 
x2  3
x
x
h( x) 
x 1
x2
g( x)  sin x
State the natural domain and range of given functions.
g ( x)  4  x 2
f ( x)  3 
h( x)  x2  3
f ( x)  3 sin x
x
Find the value of x given the value of the function.
k ( x)  3x  2 ,
k ( x)  a ,
a6
f ( x)  sin 2 x  x2  4 ,
1
x
h(4) 
2x
b  3
(use a calculator for this problem)
if x  3
h(x) 
g(x) 
f ( x)  b ,
h(4) 
h(3) 
h(t 2  5) 
if x  3
1
t 1
if t  0
if 0  t  2
t 2  1 if t  2
g(0) 
g(6) 
g(2) 