PRE$CALCULUS*HONORS*TEST*REVIEW*1.4—1.5*!
1. Determine whether the equation represents y as a function of x.
x 2 + y2 = 4
2. Evaluate f (x) = x + 8 − 2 at each value:
a. f (−8)
b.
f (1)
c.
f (x − 8)
⎧ x 2 + 2,
3. Evaluate f (x) = ⎨
⎩2x + 4,
a. f (−2)
b.
f (0)
c.
f (1)
x ≤ −1
x > −1
4. Find the value(s) of x for which f (x) = g(x) .
f (x) = x 4 − 2x 2 ,
!
g(x) = 2x 2
at each value:
!
Find the domain of the function.
5.
x 2 − 16
.
f (x) = 2
x −4
6.
f (x) =
7.
f (x) = 4 x 2 + 3x
1
3
+
2
x
x −1
In 8-9, (a) find the zeros of the function, (b) use a graphing utility to graph the
function, (c) approximate the intervals over which the function is increasing,
decreasing, or constant, (d) find the relative maximum(s) and/or minimum(s), and
(e) determine whether the function is even, odd, or neither.
!
8.
f (x) = 3x 2 + 22x − 16
9.
f (x) =
x 2 − 9x + 14
4x
!
Determine the intervals over which the function is increasing, decreasing, or
constant. Determine the domain and range.
⎧ x + 3, x ≤ 0
⎪
10. f (x) = ⎨ 3,
0<x<2
⎪2x + 1, x ≥ 2
⎩
⎧2x + 1,
11. Sketch the graph of f (x) = ⎨ 2
⎩ x − 2,
!
x ≤ −1
x > −1
.
!
⎧ 3x − 1, x < −1
⎪
12. Sketch the graph of f (x) = ⎨5,
−1 ≤ x ≤ 1.
⎪x2 ,
x >1
⎩
13. Find the surface area of a sphere in terms of its volume.
Find the difference quotient and simplify your answer.
14. For f (x) = x 3 − 5x 2 + x , find
15. For f (x) = 5x , find
!
f (x + h) − f (x)
, h ≠ 0.
h
f (x) − f (5)
,x ≠ 5.
x−5
!
Find the average rate of change of the function from x1 to x2 .
16. f (x) = x 3 − 3x 2 − x,
x1 = 1, x2 = 3
!
!
!
!
!
!
!
!
Write*the*height*h*of*the*rectangle*as*a*function*of*x.***
*
17. !
!