SME
Grade 8 Math · Problem type
Is it a function? Mapping diagram
Use this for “Each input is its output squared. Is the output a function of the input?”
Diagram
Input 4 has 2 outputs, −2 and 2: not a function.
The vertical line at x = 4 crosses 2 points: it fails the vertical-line test.
This is an example. Type your own values to start a new problem.
y₁
Output 1
example
x₁
Input 1
worked out (not typed)
y₂
Output 2
example
x₂
Input 2
worked out (not typed)
y₃
Output 3
example
x₃
Input 3
worked out (not typed)
y₄
Output 4
example
x₄
Input 4
worked out (not typed)
Formulas
x₁
=
y₁
×
y₁
(input
1
=
output
1
×
output
1)
4 = 2 × 2
x₂
=
y₂
×
y₂
(input
2
=
output
2
×
output
2)
4 = −2 × (−2)
x₃
=
y₃
×
y₃
(input
3
=
output
3
×
output
3)
9 = 3 × 3
x₄
=
y₄
×
y₄
(input
4
=
output
4
×
output
4)
1 = 1 × 1
Assumptions
•
Each pair is an input and an output. Here each input is its output times itself.
•
A function gives each input exactly one output.
•
If one input has two arrows (4 → 2 and 4 → −2), it is not a function.
•
On the graph, no vertical line crosses a function twice.
Step-by-step
WE KNOW
y₁ = 2 (output 1), y₂ = −2 (output 2), y₃ = 3 (output 3), y₄ = 1 (output 4)
FIND
input 1 (x₁), input 2 (x₂), input 3 (x₃), input 4 (x₄)
Step 1 · Find input 1 (x₁)
Use x₁ = y₁ × y₁ (input 1 = output 1 × output 1)
The input is the output times itself.
x₁
=
2
×
2
x₁
=
4
Step 2 · Find input 2 (x₂)
Use x₂ = y₂ × y₂ (input 2 = output 2 × output 2)
The input is the output times itself.
x₂
=
−2
×
(−2)
x₂
=
4
Step 3 · Find input 3 (x₃)
Use x₃ = y₃ × y₃ (input 3 = output 3 × output 3)
The input is the output times itself.
x₃
=
3
×
3
x₃
=
9
Step 4 · Find input 4 (x₄)
Use x₄ = y₄ × y₄ (input 4 = output 4 × output 4)
The input is the output times itself.
x₄
=
1
×
1
x₄
=
1
(Input
4
has
two
outputs,
2
and
−2,
so
the
output
is
not
a
function
of
the
input.)
Check
Put the numbers back in. Both sides should match.
4 = 2 × 2 ✓
4 = −2 × (−2) ✓
9 = 3 × 3 ✓
1 = 1 × 1 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.