161 Precalculus 1
Problem 1. Let
Review 1
u and v be linear functions defined as
u ( x) 2 x 3,
v( x) 3x 2.
Find the compositions
and
u v and v u . Graph the linear functions (u v)( x)
(v u )( x) in the same coordinate system.
Solution.
(u v)( x) u (v( x)
161 Precalculus 1
Review 2
In problems 1 4 consider the following quadratic function
y = x 2 + 7 x + 1.
3
Problem 1 Write the function in the standard form
y = a ( x xv ) 2 + yv
and find the coordinates of the vertex.
2
Solution. We first factor out the c
161 Precalculus 1
Review 3
Problem 1 Perform computations and present the result as a complex number in
the standard form a
bi .
(3 2i )(4 3i )
(6 5i )(5 6i )
Solution
(3 2i )(4 3i)
(6 5i )(5 6i)
Recalling that
i2
12 9i 8i 6i 2
.
30 36i 25i 30i 2
1we see
161 Precalculus 1
Review 4
Problem 1
(a) A relation is given as the set of pairs
R cfw_(1,0),(2, 1),(3,1),(1,2)
Find the domain and the range of this relation, graph the relation, and decide
whether this relation is a function.
Solution. The domain is the
161 Precalculus 1
Review 6
Problem 1 The equation of a circle is given as
x2 8x
y2 4 y 5
(a) Bring this equation to the standard form
(b) Find the center and the radius of the circle
(c) Graph the circle
Solution (a) we will complete squares using the for
161 Precalculus 1
Review 5
( x 2) x 2 ( x 1) .
Problem 1 Graph the polynomial function P( x)
Solution The polynomial is of degree 4 and therefore it is positive to the left of
its smallest real root and to the right of its largest real root. The roots of