Question

The distance in miles a bicyclist home after riding x hours is represented by the function f(x)=8x+ is the rate of change in this situation? What does the rate of change represent.

Answer 1

The rate of change for the function representing distance after x hours of bicycling is 8, which indicates a constant speed of 8 miles per hour.

Step-by-step explanation:

The function f(x) = 8x represents the distance in miles a bicyclist is from home after riding for x hours. The rate of change in this situation is 8, which is the coefficient of x in the function. This rate of change represents the constant speed at which the bicyclist is traveling. Therefore, for each hour the bicyclist rides, they will cover 8 miles. When represented on a graph of position versus time, this function would produce a straight line, indicating a uniform motion.

Answer 2

The rate of change in the function f(x)=8x is 8, which represents the bicyclist's constant speed of 8 miles per hour in this situation.

Step-by-step explanation:

The rate of change in the given function f(x)=8x, which represents the distance in miles that a bicyclist is from home after riding for x hours, is 8. This rate of change is the coefficient of x in the linear function and represents the constant speed at which the bicyclist is traveling. Therefore, the bicyclist is riding at a speed of 8 miles per hour.

To visualize this, imagine a position versus time graph where the x-axis represents time in hours, and the y-axis represents position in miles. Given that the line starts with an initial value of d=0 at t=0, it crosses the x-axis at the origin, which is the initial position. As time increases, the line will rise steadily, reflecting the uniform rate at which the distance from home increases. The slope of this line, which is the rate of change, is the speed of the bicyclist, and it represents how many miles are covered per hour ridden.