Functions Worksheet - Big Ideas Math Prealgebra: A Florida Standards Curriculum Teaching Edition Page 31
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47Identifying a Nonlinear Function
3 3
EXAMPLE
Which equation represents a nonlinear function?
y = π x
y = 4.7
○
○
A
B
4
y =
y = 4(x − 1)
—
○
○
C
D
x
You can rewrite the equations y = 4.7, y = π x, and y = 4(x − 1) in
slope-intercept form. So, they are linear functions.
4
You cannot rewrite the equation y =
—
in slope-intercept form.
x
So, it is a nonlinear function.
The correct answer is
○
.
C
Real-Life Application
4 4
EXAMPLE
Account A earns simple interest. Account B earns compound interest.
The table shows the balances for 5 years. Graph the data and compare
the graphs.
Savings Account
Account B
y
Account A
Account B
Year, t
170
Balance
Balance
160
0
$100
$100
150
140
1
$110
$110
130
2
$120
$121
Account A
120
3
$130
$133.10
110
100
4
$140
$146.41
0
5
$150
$161.05
0
1
2
3
4
5
6
7
t
Year
Both graphs show that the balances are positive and increasing.
The balance of Account A has a constant rate of change of $10.
So, the function representing the balance of Account A is linear.
The balance of Account B increases by different amounts each year.
Because the rate of change is not constant, the function representing
the balance of Account B is nonlinear.
Does the equation represent a linear or nonlinear function? Explain.
Exercises 12–14
4x
4. y = x + 5
5. y =
6. y = 1 − x
2
—
3
Section 6.4
Comparing Linear and Nonlinear Functions
269
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