Pre Calc
Class review
Name __________________
Period _____________
1) Let A = {a, b, c, d} and B = {-4, -2, 0, 2,
4}. Which set of ordered pairs represents
a function from A to B?
6) F(x) is the original function. Explain the
transformations used to obtain the graph g(x).
f (x)
g (x)
(a) (b, 4), (c, 2), (d , 4), (d , 0)
(b) (a, − 4), (b, − 2), (b, 0), (c, 2)
(c) (a, 0), (a, 2), (b, − 2), (b, − 4)
(d ) (a, 4), (b, − 4), (c, 2), (d , 2)
(e) None of these
(a) g ( x) = f ( x − 2) + 1
(b) g ( x) = f ( x + 2) − 1
(d ) g ( x) = f ( x − 1) − 2
⎧3x + 4,
x≥2
(c) g ( x) = f ( x + 1) − 2
⎩ x + 1,
x<2
(e) None of these
2) Given f ( x) = ⎨
2
7) Identify the graph of:
Find f(3)
(a ) 13
⎧2 x + 1, x ≤ 1
f ( x) = ⎨ 2
x >1
⎩x
(b) 10
(c ) 5
(d ) 3
(e) None of these
3) Given f ( x) = x 2 + 3x + 4 , find f(x+2) – f(2)
(a)
(b)
___________________________________
4) Find all real values of x such that f(x) = 0:
(Find the zeros)
f ( x) = x( x 2 − 9 )
(c)
(d)
(e) None of these
(a) ± 3
(b) 3
(c) 0, ± 3
(e) None of these
(d ) 0, 3
9) Given f ( x) = x − 2 and
( f + g )(−3)
g ( x) = 4 − 2 x
find
5) For what values of x does f ( x) = g ( x) ?
f ( x) = 3x + 1,
g ( x) = x 2 − 3
10) What is the conjugate of −2 − i 5 ?
__________________________________
_________________________________
11) The graph below is a transformation of
the graph of f(x) = |x|. Find an equation for
the function.
15) Find the domain of h( x) =
1
x + 3x + 2
2
__________________________________
16) Given
f ( x) = 2 x 3 − 1
find f −1 ( x)
__________________________________
(a) g ( x) = 14 x + 1 − 2
(b) g ( x) = −4 x − 1 − 2
(c) g ( x) = − 14 x − 2 − 1
(d ) g ( x) = 4 x − 2 − 1
(a ) f ( x) = x + 5
g ( x) = x − 5
(e) g ( x) = −4 x − 2 − 1
12) Find the equation of the function whose
graph is a horizontal shift 9 units to the right
and a vertical shift 3 units down of the graph
f ( x) = 3 x
(a) g ( x) = 3 x + 9 − 3
(b) g ( x) = 3 x − 9 + 3
(c ) g ( x ) = x − 3 − 9
(d ) g ( x) = x − 9 − 3
3
17) Determine which sets of functions are not
inverses of each other.
3
( e) g ( x ) = 3 x + 9 + 3
13) Given f ( x) = 1 and g ( x) =
x2
find ( f g )(x)
x +4
2
__________________________________
14) The growth of the number of employees
hired by a company has been linear for the
past ten years, starting at 323 ten years ago
and currently standing at 393. Estimate the
number of employees that will be employees
three years from now.
__________________________________
(b) f ( x) = x 3
g ( x) = 3 x
x+2
4
g ( x) = 4 x − 2
(c ) f ( x ) =
(d ) All of the above are inverses of each other.
(e) None of the above are inverses of each other.
18) Tracey went for a long walk at a rate of 2
miles per hour. Three hours later, her
brother Richard rode after her on a tandem
bike at a rate of 7 mile per hour.
a. How long had Tracey been walking when
Richard met her?
b. How far had she walked when they met?
c. How long will it take them to ride back on
the bike traveling at 6 miles per hour

xgf  xfg  f . If xgf  = x and xfg  = x, then

Lecture 11: Positive semidefinite matrix