Chapter 3.2, Problem 15E

To determine

To calculate: To describe and correct the error in determining whether the table or graph represents a linear function

Answer to Problem 15E

Graph represents non-linear function

Explanation of Solution

Given: Table is

x	2	4	6	8
y	4	16	64	256

Formula Used:

Linear functions are polynomials with degree of $1$ and have constant slopes. Graph of linear function is a straight line

Non-linear functions are polynomials with degree of more than $1$ and have a slope that varies between points. Graph of non-linear function is a curved line

Calculation:

Table is

x	2	4	6	8
y	4	16	64	256

Calculate the slope for the above:

  $m_1=\frac{16-4}{4-2}=\frac{6}{2}=3$

  $m_2=\frac{64-16}{6-4}=\frac{48}{2}=24$

  $m_3=\frac{256-64}{8-6}=\frac{192}{2}=96$

Since the slope is constant, thus it’s a non-linear function

Conclusion:

Hence, graph represents non-linear function