Question

Which of the following graphs represents a one-to-one function?

Answer 1

Answer:Graph 4

Step-by-step explanation:

To find a function is one to one we have to perform vertical and horizontal line test

And if it clears the test then it would be one to one

Graph 1 doesn't clears horizontal line test as if we draw a horizontal line it will cut the curve two times with same value of Y

Same is the case with Graph 2 , as if we draw a horizontal line it will cut the graph at two same values!

So graph2 also eliminated!

Graph 3 is an ellipse along y axis so it so the horizontal line cuts the ellipse two times with same values of y and if we draw a vertical line then, also it will cut the ellipse two times with same value of x

So option 3 eliminated!

But in Graph 4 if we draw a horizontal or vertical line it will cut the given points with same value of y or x

So, Graph 4 represents one to one function.

Hope it helps!!!

Answer 2

Answer:

The 4th graph is one to one.

Step-by-step explanation:

Consider the provided graph.

Horizontal line test: If a horizontal line intersects a function's graph more than once, then the function is not one-to-one.

Remember: The function y = f(x) is a function if it passes the vertical line test.

Now consider the provided graph.

Graph 1: Draw the horizontal line as shown in figure 1.

Here, we can observe that the horizontal line intersect the graph more than once, therefore first graph is not one-to-one.

Graph 2: The second graph is not a function as it doesn't passes the vertical line test as shown in figure 2.

Graph 3: Draw the horizontal line as shown in figure 3.

Here, we can observe that the horizontal line intersect the graph more than once, therefore third graph is not one-to-one.

Graph 4: Draw the horizontal line as shown in figure 4.

Here, we can observe that the horizontal line intersect the graph not more than once, therefore fourth graph is one-to-one.

The fourth graph is one to one