Practice Nonlinear Relationship in Math

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

A relationship between two quantities where the rate of change is not constant—the graph is curved, not a straight line.

Not a straight line—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). Linear or nonlinear? Identify the rule.

Example 2

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

Example 3

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

Example 4

medium
For y=x2, calculate values at x=−2,−1,0,1,2. Is the graph symmetric?

Example 5

easy
Is y=x linear or nonlinear?

Example 6

easy
Linear or nonlinear: area of a square as a function of its side, A=s2?

Example 7

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

Example 8

medium
Does y=2x ever have a constant rate of change? Check x=0→1 and x=1→2.

Example 9

easy
Does the volume of a sphere V=43πr3 grow linearly with radius?

Example 10

medium
Sketch the difference: which grows faster from x=0 to x=10 — y=2x (linear) or y=2x (exponential)?

Example 11

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

Example 12

hard
Determine whether y=2x is linear or nonlinear by examining the ratio yn+1/yn for x=0,1,2,3.

Example 13

easy
Linear or nonlinear: y increases by 3 each time x increases by 1?

Example 14

medium
Distance fallen under gravity follows d=4.9t2. Linear or nonlinear in t?

Example 15

medium
Data: (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). Is the change a constant difference or constant ratio?

Example 17

easy
Is the relationship y=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 h²). Find for which h Plan B first exceeds Plan A.

Example 19

medium
For y=x2, find the first differences and second differences for x=0,1,2,3,4.

Example 20

easy
Is the graph of y=x3 a straight line?
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