Maths-

General

Easy

Question

# Sketch a graph modelling a function for the following situation:

A dog is sleeping when he hears the cat “meow” in the next room. He quickly runs to the next room where he slowly walks around looking for the cat. When he doesn’t find the cat, he sits down and goes back to sleep. Sketch a graph of a function of the dog’s speed in terms of time.

Hint:

### Figure out slope of the graph with respect to situations given.

## The correct answer is: line y = 0 which is parallel to x – axis and has slope = 0

### SOL – Let dog’s speed = y

Time taken = x

Acc. to the question, dog was sleeping when time, x = 0 , speed, y = 0

Then, he quickly runs to the next room i.e. speed is increasing over time. Since he moved quickly, implies that rate of change is very high.

Slope is positive and line is very steep

Then, he slowly walks around looking for the cat. i.e. there is a sudden decrease in the speed.

A line parallel to y – axis will be drawn to a point where speed is less.

And then he walks around looking for the cat i.e., speed is same over time

A line parallel to x – axis is drawn

Further, he sits down and goes back to sleep i.e. speed is 0

Since speed suddenly drops to 0, so line x = 0 which is parallel to y – axis and then line y = 0 which is parallel to x – axis and has slope = 0

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