Question

Tell whether each graph is a function and justify your answer. Which graph is not a good representation of a real world situation? Explain.

## The correct answer is: 2, 6 and 8

*Hint:*

An equation of the form y = f(x) is called a function if there is a unique value of y for every value of x. In other words, every value of x must have one value of y. We can check if the graph is a function by the vertical line test. A graph represents a function if any vertical line in the xy plane cuts the graph at maximum one point.

*Step by step solution:*

The first graph is

We check if the graph is a function by vertical line test.

When we draw a vertical line at x = 4, it cut the graph at 3 points.

Thus, graph A is not a function.

Graph B is

We can observe that any vertical line on the plane cuts the graph at maximum one point.

Thus, the above graph is a function.

In graph A, at time t = 4, we can see that d has three values, which are 2, 6 and 8.

This means that at the same time t=4, the distances travelled are 2, 6 and 8, which is physically impossible. There can be only one value of distance associated with a value of time which is the case in graph B.

Thus, graph A is not a good example of a real world situation.

*Note:*

In a function, every value of x must have one value of y. When we draw a vertical, it cuts x axis at one point, we take that point to be x. If the vertical line cuts the graph at two points, then it gives two values of y for one value of x. This does not represent a function.

### Related Questions to study

### A train leaves the station at time . Travelling at a constant speed, the train travels 360 kilometers in 3 hours.

a) Write a function that relates the distance travelled ,d to the time, .

b) Graph the function and tell whether it is a linear function or non linear function.

There are other ways to determine whether a function is linear or not, like, checking if the slope is equal between each of the points or if the equation can be written in the form of y = ax + b, where a and b are constants.

### A train leaves the station at time . Travelling at a constant speed, the train travels 360 kilometers in 3 hours.

a) Write a function that relates the distance travelled ,d to the time, .

b) Graph the function and tell whether it is a linear function or non linear function.

There are other ways to determine whether a function is linear or not, like, checking if the slope is equal between each of the points or if the equation can be written in the form of y = ax + b, where a and b are constants.

### Do the ordered pairs plotted in the graph below represents a function? Explain.

In a function, every value of x must have one value of y. When we draw a vertical, it cuts x axis at one point, we take that point to be x. If the vertical line cuts the graph at two points, then it gives two values of y for one value of x. This does not represent a function.

### Do the ordered pairs plotted in the graph below represents a function? Explain.

In a function, every value of x must have one value of y. When we draw a vertical, it cuts x axis at one point, we take that point to be x. If the vertical line cuts the graph at two points, then it gives two values of y for one value of x. This does not represent a function.

### The relationship between the number of hexagons, , and the perimeter of the figure they form, , shown in the graph. Is the perimeter of the figure a function of the number of hexagons? Explain.

In a function, every value of x must have one value of y. When we draw a vertical, it cuts x axis at one point, we take that point to be x. If the vertical line cuts the graph at two points, then it gives two values of y for one value of x. This does not represent a function.