Question

The table and graph represents two different bus to come showing the cost as a linear function of the number of people in the group. Which description best compares the two functions?

Answer 1

The functions have the same initial value. The table goes up by 10 per person so at 0, it would be 35 and on the graph, it is 35 at 0

Answer 2

The description that best compares the two functions is:

The functions have the same initial value.

Explanation:

We are given the table for Tour 1 as:

People cost($)

1 45

2 55

3 65

4 75

The function that represents these points is given by:

y=10x+35

where x represent people and y represent the cost of x people.

This means that the rate of change is: 10

and initial value i.e. when x=0 is: 35

Tour 2 is given by:

People Cost ($)

0 35

1 50

2 65

3 80

4 95

Hence, we see that the initial value is: 35

and the rate of change of the function is: 15

(

Since,

`(50-35)/(1-0)=(65-50)/(2-1)=(80-65)/(3-2)=(95-80)/(4-3)=15` )

• Hence, we see that the rate of change for Tour 2 is greater than Tour 1.