Question

Wendy played her favorite video game for 8 hours last week. Today, Wendy's parents restricted her to 6 additional hours each week for the next 9 weeks. Create the function, f(x), that models Wendy's total video game time, and explain what each number in the situation represents graphically, using complete sentences

Answer 1

This function will be a linear function so on the horizontal axis (x) you will have weeks, and in the vertical axis (y) you will find hours. Week 0 will be 8, because its the initial amount of hours.
Therefore, the equation is: f(x) = 6x+8

Answer 2

Answer: The required function is,

f(x) = 8 + 6x

Where, x is the number of weeks after last week,

f(x) is the total time of gaming,

8 represents the number of hours of playing last week.

6 is the number of hours of playing each week after last week,

Explanation:

Given,

The number of hours Wendy played the video game last week = 8,

Since, after this week, he is playing the video game for 6 hours each week,

Thus, the number of hours he played for x weeks = 6x,

Hence, the total number of hours = 8 + 6x

Here, f(x) models his total video game time,

⇒ f(x) = 8 + 6x

Graphing :

In the coordinate plane x-axis represents the number of weeks,

While, y-axis represents the total number of hours.