Question

Peter played his favorite video game for 10 hours last week. Today, Peter's parents restricted him to 5 additional hours each week for the next 8 weeks. Create the function, f(x), that models Peter's total video game time, and explain what each number in the situation represents graphically, using complete sentences.

Answer 1

Let

x--------> the number of weeks

f(x)------->Peter's total video game time in hours

we know that

$f(x)=5x+10$

The domain of the function is the interval [0, 8]

The y-intercept of the function is the point (0,10)

$10$ is the initial amount of hours Peter's played

The slope of the function is equal to $m=5 \frac{hours}{week}$

Is the rate at how many hours he is playing extra each week

using a graph tool

see the attached figure

Answer 2

F(x)=5x+10
x only positive whole numbers
0<x<8
f(x)= how many hours he played in the x week or y value
5 the rate at how many hours he is playing extra each week or slope
x the number of the week or time
10 is the y intercept or the initial amount of hours he played