Average Rate of Change pt 2

What does the slope of a secant line represent?

• The instantaneous rate of change of a function.

• The average rate of change of a function between two points.

• The maximum value of a function.

• The y-intercept of a function.

Which formula is used to calculate the slope of a line given two points (x1, y1) and (x2, y2)?

• m = (x2 - x1) / (y2 - y1)

• m = y1 - y2 / x1 - x2

• m = (y2 - y1) / (x2 - x1)

• m = (x1 + x2) / (y1 + y2)

In the animation showing secant and tangent lines, what does the red secant line represent?

• The instantaneous slope of the function at a single point.

• The overall shape of the function.

• The average rate of change of the black function between two points.

• The derivative of the function.

As the secant line animates and its points move along the function, what happens to the average rate of change?

• It remains constant.

• It always increases.

• It always decreases.

• It changes, reflecting the varying steepness of the function.

If you travel 380 miles in 5.5 hours, what is your average speed?

• Approximately 65.2 mph

• Approximately 69.1 mph

• Approximately 72.5 mph

• Approximately 75.0 mph

On a graph comparing time to distance traveled, what does a steeper section of the graph indicate?

• The traveler is moving slower.

• The traveler is stopped.

• The traveler is moving faster.

• The traveler is moving backward.

On a distance-time graph, what does the slope of a secant line connecting two points represent?

• The instantaneous speed at the starting point.

• The total distance traveled.

• The average speed between those two points.

• The maximum speed achieved during the trip.

Based on the distance-time graph, how does the average speed from 2 to 3 hours compare to the average speed of the entire trip (0 to 5.5 hours)?

• The average speed from 2 to 3 hours is greater than the average speed of the entire trip.

• The average speed from 2 to 3 hours is less than the average speed of the entire trip.

• The average speed from 2 to 3 hours is the same as the average speed of the entire trip.

• It is impossible to compare the average speeds from the given graph.

What function is being analyzed to determine its average rate of change?

• f(x) = x^2 + 1

• f(x) = x + 1

• f(x) = x^2 - 1

• f(x) = 2x + 1

For the function f(x) = x^2 + 1, what are the corresponding y-values when x = 0 and x = 3?

• y=0, y=3

• y=1, y=10

• y=1, y=9

• y=0, y=9