IDENTIFY LINEAR AND NONLINEAR FUNCTIONS WORKSHEET

Questions 1-4 : Determine whether each table represents a linear or nonlinear function.

Question 1 :

Question 2 :

Question 3 :

Question 4 :

Questions 5-8 :Determine whether each graph represents a linear or nonlinear function.

Question 5 :

Question 6 :

Question 7 :

Question 8 :

Questions 9-13 : Determine whether each equation represents a linear or nonlinear function. Remember that all linear functions can be written in the slope-intercept form, that is y = mx + b.

Question 9 :

y = 5x + 2

Question 10 :

y = 3(x - 4)

Question 11 :

y = x/2 + 5 

Question 12 :

y = 2/x - 3 

Question 13 :

y = -5x

Question 14 :

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.

Question 15 :

The table shows the volume V (in cubic feet) of a cube with a side length of x feet. Does the table represent a linear or nonlinear function? Explain.

Question 16 :

The table shows the cost y (in dollars) of x pounds of sunflower seeds.

a. What is the missing y-value that makes the table represent a linear function?

b. Write a linear function that represents the cost y of x pounds of seeds.

1. Answer :

In the above table, as x increases by 2, y increases by 3. The rate of change is constant. So, the above table represents a linear function.

2. Answer :

In the above table, as x increases by 2, y increases by a greater amount each time. The rate of change is NOT constant. So, the above table represents a nonlinear function.

3. Answer :

In the above table, as x increases by 3, y increases by a greater amount each time. The rate of change is NOT constant. So, the above table represents a nonlinear function.

4. Answer :

In the above table, as x increases by 4, y decreases by 2 each time. The rate of change is constant. So, the above table represents a linear function.

5. Answer :

The above graph is a straight line. So it represents a linear function.

6. Answer :

The above graph is not a straight line. So it represents a nonlinear function.

7. Answer :

The above graph is a straight line. So it represents a linear function.

8. Answer :

The above graph is not a straight line. So it represents a nonlinear function.

9. Answer :

y = 5x + 2

The above function is in slope-intercept form.

So, it represents a linear function.

10. Answer :

y = 3(x - 4)

The above function can be written in slope-intercept form.

y = 3(x - 4)

y = 3x - 12

So, it represents a linear function.

11. Answer :

y = x/2 + 5 

The above function can be written in slope-intercept form.

y = x/2 + 5 

y = (1/2)x + 5

y = 0.5x + 5

So, it represents a linear function.

12. Answer :

y = 2/x - 3 

The above function cannot be written in slope-intercept form.

So, it represents a nonlinear function.

13. Answer :

y = -5x

y = -5x + 0

The above function is in slope-intercept form.

So, it represents a linear function.

14. Answer :

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.

15. Answer :

Changes in x is the same, it differs by 1. Changes in y is not the same. Then it is not a constant function.

16. Answer :

Solution :

a)  Since it is linear function, the rate of change 

= 2.80/2

= 1.40

When x = 3, y = 2.80 + 1.40

= 4.2

b) y = 1.4x

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