Posted: November 13th, 2015

Pre-calculus

Pre-calculus

1. Find the domain of f(x):
a) f(x) = 2x
3 + 5
x
2 + x – 6
b) f(x) = v
3 – x –
v
2 + x
c) f(x) =
?
??
??
1
x+8 x = 0
cos x 0 < x < 2p
2 –
v
x x = 2p
2. Classify each function as a power function, polynomial, rational function, algebraic function,
trigonometric function, exponential function or logarithmic function. Give a short
explanation for each answer.
a) y = p
x
.
b) y = x
p
.
c) y = x
2
(2 – x
3
).
d) y = tan(t) – cos(t).
e) y =
s
1 + s
.
f) y =
v
x
3 – 1
1 + v3 x
.
3. Let f(x) = 3x – 2, g(x) = v
x and h(x) = x
x – 1
.
a) Find f ? g(x).
b) Find f ? h(x).
c) Find h ? g(x).
d) Find an example of r(x) and s(x) so that r ? s(x) = 2e
x-5
.
4. A cell phone plan has a basic charge of $35 a month. The plan includes 400 free minutes
and charges 10 cents for each additional minute of usage. Write the monthly cost C as a
function of the number x of minutes used and graph C as a function of x for 0 = x = 600.
What is the domain and range of C(x).

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