4. Functions and Relations
Middle Years
4.01 Sign diagrams
Worksheet
1
Construct a sign diagram for each of the following linear functions:
a
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
b
-2
-1
1
2
x
-4
-3
-2
-1
1
2
3
4
y
c
-2
-1
1
2
3
4
5
6
x
-4
-3
-2
-1
1
2
3
4
y
d
-6
-5
-4
-3
-2
-1
1
2
x
-4
-3
-2
-1
1
2
3
4
y
2
Construct a sign diagram for each of the following quadratic functions:
a
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
b
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
c
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
d
-4
-3
-2
-1
1
2
3
4
x
-2
-1
1
2
3
4
5
6
7
8
y
3
Construct a sign diagram for each of the following cubic functions:
a
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
b
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
c
-5
-4
-3
-2
-1
1
2
3
4
5
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
d
-8
-6
-4
-2
2
4
6
8
x
-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
10
y
4
Construct a sign diagram for the following hyperbolas:
a
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
b
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
c
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
d
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
5
For each of the following sign diagrams, sketch a possible corresponding function:
a
b
c
d
e
f
6
Consider the inequality: 2x-10 \lt 0.
a
Solve the equation 2x-10 = 0 for x.
b
Construct a sign diagram for the function f(x)=2x-10.
c
Hence, solve the inequality.
7
Consider the inequality: 3x^2-75 \lt 0.
a
Solve the equation 3x^2-75 = 0 for x.
b
Construct a sign diagram for the function f(x)=2x-10.
c
Hence, solve the inequality.
8
Use sign diagrams to solve the following inequalities:
a
3x+12 \gt 0
b
8x-24 \leq 0
c
6x+30 \geq 0
d
2x \gt 42
e
x^2 - 1 \gt 0
f
x^2 -9 \lt 0
g
x^2 - 25 \geq 0
h
10x^2 - 1000 \gt 0
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