Question

the table shows a function. is the function linear or nonlinear? linear nonlinear

Explanation:

Step1: Identify x and y values

From the table, the points are \((0, 2)\), \((3.13, 3.14)\), and \((10, 5.14)\) (assuming the numbers are \(x = 0,y = 2\); \(x\approx3.13,y\approx3.14\); \(x = 10,y\approx5.14\)).

Step2: Calculate the slope between first and second point

Slope formula: \(m=\frac{y_2 - y_1}{x_2 - x_1}\)
For \((x_1,y_1)=(0,2)\) and \((x_2,y_2)=(3.13,3.14)\)
\(m_1=\frac{3.14 - 2}{3.13 - 0}=\frac{1.14}{3.13}\approx0.364\)

Step3: Calculate the slope between second and third point

For \((x_2,y_2)=(3.13,3.14)\) and \((x_3,y_3)=(10,5.14)\)
\(m_2=\frac{5.14 - 3.14}{10 - 3.13}=\frac{2}{6.87}\approx0.291\)

Step4: Compare the slopes

Since \(m_1\approx0.364\) and \(m_2\approx0.291\) are not equal, the function is nonlinear.

Answer:

nonlinear