Problem :
Classify each of the following as a function of x, a onetoone function, or neither:
a) y = 2x^{4}  6
b) y =
c) y = 4x + 7
d) x = y^{2}
a) A function of
x. Each
x is assigned one
y. Since each
y is assigned to
two
x values, this is not a onetoone function:
Figure %:Passes vertical line test. Classified as a function
Figure %:Fails horizontal line test. Not a onetoone function
b) Also a function of
x. Not a onetoone function
Figure %:
y =
c) A onetoone function. Passes vertical and horizontal line tests.
Figure %:y = 4x + 7
d) Not a function of
x. Fails the vertical line test
Figure %:x = y^{2}
Problem :
What is the domain and range of each of the following functions?
a) y = 3sin(2x)
b) y =
a) Domain=
( ∞,∞); Range=
[ 3, 3]
b) This function can also be expressed as
y = . This function
looks identical to its reduced form,
y = x + 3, except that it is undefined at
x = 3.
Domain=
x≠3; Range=
y≠6
Figure %:Graph of
y =
Problem :
Let
f (x)   = 4x  2 

g(x)   = x^{2} 

a) Find
fog(2)
b) Find
gof(2)
a)
f (g(2)) = f (2^{2}) = f (4) = 4(4)  2 = 14
b)
g(f (2)) = g(4(2)  2) = g(6) = 36
Problem :
Consider the following piecewise function:
f (x) = 

Find the following:
a)
f ( 1)
b)
f (5)
c)
f (10)
a)
f ( 1) = ( 1)^{3}  2( 1) =  1  ( 2) = 1
b)
f (5) = (5)^{3}  2(5) = 125  10 = 115
c)
f (10) = 17(10) = 170
Problem :
Is this function even, odd, or neither?
a) f (x) = cos(x)
b) f (x) = sin(x)
c) f (x) = tan(x)
d) f (x) = cos(x + )
a) Even,
cos( x) =  cos(x)
b) Odd,
sin( x) =  sin(x)
c) Odd,
tan( x) =  tan(x)
d) Neither. Shifting
cos(x) to the right by
destroys the symmetry with
respect to the
yaxis.