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 

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.

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