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:
b) Also a function of x. Not a one-to-one function
c) A one-to-one function. Passes vertical and horizontal line tests.
d) Not a function of x. Fails the vertical line test
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
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 y-axis.