Pre-Calculus - Graphing Review
Graph standard, then describe using translation.
1)
2)
Given a standard parabola graph of y = x2; explain what happens to this graph using
the following information:
a)
Graph y = x2
d)
y + 9 = 1/2 (x - 1)2
g)
1
x " 4 = " ( y + 2)2
5
b)
y - 2 = (x + 3)2
c)
y + 3 = 2(x + 4)2
e)
3
y = " ( x + 2)2
5
f)
x = y2
!
Given a standard absolute value graph of y = |x|; explain what happens to this
graph using the following information:
!
3)
a)
Graph y = |x|
b)
y = 2|x|
c)
1
y "4 =" x +2
3
d)
y + 2 = -|x - 5|
e)
x = |y|
f)
x = -3 |y - 2|
Given a standard rectangular hyperbola
using the following information:
4)
5)
!
1
x
b)
y=
1
!
x+2
c)
y=
1
+3
x
"1
x "1
f)
y=
3
2x + 3
g)
y=
1
x2
a)
Graph
e)
y=
!
!
1
; explain what happens to this graph
x
!
!
d)
y ="
1
x
!
Given a standard square root equation
!
!
using
the following!information:
x ; explain what happens to this graph
a)
Graph y =
x
b)
y = x+2
!
c)
y = 5" x
e)
y =2+ x "4
f)
y =2 x+4
g)
y = "2 " 3 3 " x
!
!
!
!
!
d)
y = " x +1
!
Given a standard cubic equation x3; explain what happens to this graph using the
following information:
a)
Graph y = x3
d)
y = 2(x - 4)3 - 3
!
b)
y = (x + 2)3
e)
y=
1 3
x
4
c)
y = -(x + 2)3 + 2
6)
Given a standard cube root equation
the following information:
a)
Graph y =
d)
y = 23 x
3
x
7)
d)
10)
!
y = 13 3 x
!
!
a)
f(x) ± c
d)
c*f(x); where 0 < c < 1
b)
f(x±c)
e)
-f(x)
c)
c*f(x); where c > 1
Graph the following lines:
y=x
b)
y=x-2
c)
y = 2x - 3
3
y =" x+4
5
d)
e)
y=
2
5
x"
3
2
Graph the following piecewise functions:
% x + 2 if
'
if
a) f (x) = & x 3
'
(#x + 3 if
!
e)
y = 3 x "1
c)
Given y = f(x) and c > 0, summarize problems 1-6 with respect to the basic info below:
a)
9)
y =3 x "2
!
!
8)
x ; explain what happens to this graph using
b)
!
!
3
$ x2 " 4
&
f ( x) = % 2 " x
&' 1
% x " 3 if
'
2
if
b) f ( x) = & "x
'"x + 4 if
(
x " #1
x <1
x $1
if
x!
#2
if
x =2
$
if
& 2
&
f ( x) = % 2x
if
e)
& 1
&'7 # x if
3
!x # "2
"2 < x < 1 c)
x $1
x <1
!
1" x " 3
x >3
! $ x 2 "1
&
f ( x) = % x + 1 if
&' 2
if
$ x + 2 if
&
if
f) f ( x) = % "x
& 3x if
'
x # "1
x = "1
x < "4
"4 # x # 5
x >5
Given a standard greatest integer function of y = [x]; explain what happens to this
graph using the following information:
!
!
a)
Graph y = [x]
e)
y = [2x] - 1
b)
y = [3x]
f)
y = [-x]
c)
y = [x] + 3
d)
"1 %
y = $ x'
#2 &
g)
y = [x - 3]
h)
y = 4[x]
11)
Graph the following rational expressions.
a)
y=
12)
Graph these polynomials on your calculator – include window, y-intercept, zeros,
and max / min.
a)
y = 4x3 - 12x2 - x + 3
!
5x + 7
2x "1
b)
y=
x2 " x " 6
x 2 + 3x + 2
!
c)
y=
!
( x " 2)( x " 3)
( x + 1)( x " 3)( x " 5)
!
b)
y = x4 - 4x3 - 7x2 + 34x - 24
d)
y=
( x "1)( x + 3)
( x + 2)( x "1)( x " 4)
!
c)
y = 9x5 - 94x3 + 27x2 + 40x – 12