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Problems for "Brief Review of Functions"

Problems for "Brief Review of Functions"

Problems for "Brief Review of Functions"

Problems for "Brief Review of Functions"

Problems for "Brief Review of Functions"

Problems for "Brief Review of Functions"

Problem : Classify each of the following as a function of x , a one-to-one 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 one-to-one function:
Figure %:Passes vertical line test. Classified as a function
Figure %:Fails horizontal line test. Not a one-to-one function

b) Also a function of x . Not a one-to-one function
Figure %: y =

c) A one-to-one 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 f o g (2)
b) Find g o f (2)


a) f (g(2)) = f (22) = 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 y -axis.