Practice Nonlinear Relationship in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A relationship between two quantities where the rate of change is not constantβ€”the graph is curved, not a straight line.

Not a straight lineβ€”it curves. Compound interest grows faster and faster.

Showing a random 20 of 50 problems.

Example 1

medium
Table (x,y)=(0,1),(1,3),(2,9),(3,27)(x,y)=(0,1),(1,3),(2,9),(3,27). Linear or nonlinear? Identify the rule.

Example 2

medium
Is the perimeter of a square, P=4sP = 4s, linear or nonlinear in ss?

Example 3

medium
For y=x2+3y = x^2 + 3, compute the rate of change from x=0x=0 to x=1x=1, and from x=2x=2 to x=3x=3.

Example 4

medium
For y=x2y = x^2, calculate values at x=βˆ’2,βˆ’1,0,1,2x = -2, -1, 0, 1, 2. Is the graph symmetric?

Example 5

easy
Is y=xy = \sqrt{x} linear or nonlinear?

Example 6

easy
Linear or nonlinear: area of a square as a function of its side, A=s2A = s^2?

Example 7

challenge
Data (x,y)=(1,2),(2,6),(3,12),(4,20)(x,y)=(1,2),(2,6),(3,12),(4,20). Show it is nonlinear and find a rule.

Example 8

medium
Does y=2xy = 2^x ever have a constant rate of change? Check x=0β†’1x=0\to1 and x=1β†’2x=1\to2.

Example 9

easy
Does the volume of a sphere V=43Ο€r3V = \tfrac{4}{3}\pi r^3 grow linearly with radius?

Example 10

medium
Sketch the difference: which grows faster from x=0x = 0 to x=10x = 10 β€” y=2xy = 2x (linear) or y=2xy = 2^x (exponential)?

Example 11

hard
For y=1/xy = 1/x, calculate yy at x=1,2,4,8x = 1, 2, 4, 8. Is the rate of change increasing or decreasing?

Example 12

hard
Determine whether y=2xy = 2^x is linear or nonlinear by examining the ratio yn+1/yny_{n+1}/y_n for x=0,1,2,3x = 0, 1, 2, 3.

Example 13

easy
Linear or nonlinear: yy increases by 33 each time xx increases by 11?

Example 14

medium
Distance fallen under gravity follows d=4.9t2d = 4.9 t^2. Linear or nonlinear in tt?

Example 15

medium
Data: (1,3),(2,5),(3,7),(4,9)(1,3),(2,5),(3,7),(4,9). Linear or nonlinear? Give the equation if linear.

Example 16

medium
Table (x,y)=(0,1),(1,2),(2,4),(3,8)(x,y)=(0,1),(1,2),(2,4),(3,8). Is the change a constant difference or constant ratio?

Example 17

easy
Is the relationship y=7xβˆ’4y = 7x - 4 linear or nonlinear?

Example 18

hard
Two plans: Plan A pays $20 + $5/hour; Plan B pays $2 per hour worked squared ($2 hΒ²). Find for which hh Plan B first exceeds Plan A.

Example 19

medium
For y=x2y = x^2, find the first differences and second differences for x=0,1,2,3,4x = 0, 1, 2, 3, 4.

Example 20

easy
Is the graph of y=x3y = x^3 a straight line?
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