Question

Two linear functions are shown below. Compare each fuoction to answer the questions. Function 2: Function 1: -11 8 -7 13 3 Ng -3 18 Part A: What is the rate of change for Function 1? Part B: What is the rate of change for Function 2? Part C: Which function has the greater rate of change?

Answer 1

The rate of change of a linear functions is given by:

`m=(y_2-y_1)/(x_2-x_1)`

where (x1,y1) and (x2,y2) are points through the graph.

Function 1.

From the table we have that the functions passes through the points (-11,8) and (-7,13), pluggin the values in the formula above we have:

`\begin{gathered} m=(13-8)/(-7-(-11)) \\ m=(5)/(11-7) \\ m=(5)/(4) \end{gathered}`

Therefore the rate of change of functions 1 is 5/4

Function 2.

From the graph we notice that the functions passes through the points (-3,-4) and (1,-1), hence:

`\begin{gathered} m=(-1-(-4))/(1-(-3)) \\ m=(-1+4)/(1+3) \\ m=(3)/(4) \end{gathered}`

Therefore the rate of change of function 2 is 3/4.

Comparing both rates of change we conclude that Function 1 has the greater change of rate.