Question

Which graph shows the equation c = 10+ 3t, where c is the total cost of going to the carnival and t is the number of $3 tickets purchased?

Answer 1

Answer: see the attached graph.

Explanation:

The given equation, c = 10+ 3t, is a linear function, which means that its graph is a line.

The slope of such graph is constant; it is the coefficient of the independent variable (t in this case).

The dependent variable is c, the total cost of going to the carnival.

The constant term, 10 in this case, is a fixed fee (the initial value of the function, when t = 0).

To graph such function you follow these steps:

•    Draw two perpendicular axis: the horizontal and the verical axis.

•    Label the horizontall axis with the name and units of the independent variable: number of tickets.

•    Label the vertical axis with the name and units of the dependent variable: cost in $.

•    Set the domain and range of the function.

             Domain: poossible values of t. The whole numbers [0, 1, 2, 3, ...]

             Range: whole numbers greater than or equal to 10 (since t is greater than or equal to 0) growing from 3 in 3: [10, 13, 16, 19, 22 ...]

•    Note that the function is discrete (not continuos)

•    Choose an adequate scale and do marks on every axis: in this case I will do marks of 1 unit each.

•    Mark the initial value, i.e. the cost when t = 0, which is:  c = 10 + 3t = 10 + 3(0) = 10 + 0 = 10

•    Mark other points. You may use this table:

            t              c($)

            0             10

            1              13

            2             16

            3              19

Finally, do not forget to add the title of the graph: cost of going to the carnival

With that information, you may understand the attached graph, which is just a sketch that shows some of the above mentioned features.

Answer 2

we have

$c = 10+ 3t$

where

c---------> is the total cost of going to the carnival

t---------> is the number of $\ 3$ tickets purchased

we know that

the domain of the function is the interval---------------> [0,∞)

Because the number of tickets can not be negative

The range of the function is the interval-------------> [10,∞)

Because the total cost can not be negative

using a graph tool

see the attached figure

The answer in the attached figure