Lesson video

Hi, I'm Ms. Davies.

In this lesson, we're going to be looking at the graphs of reciprocal functions.

A function is given by the equation y equals 10 divided by x.

Going to work out the value of y when x is equal to 10.

If we calculate 10 divided by 10, this gives us one.

When x is equal to negative two, we would do the calculation 10 divided by negative two.

This gives a solution of y is equal to negative five.

Next we're going to divide 10 by 0.

4.

This gives a solution of y is equal to 25.

Use your calculator to work out the value of y when x is equal to zero, what do you notice? We're going to complete the table of values for the function y is equal to 10 divided by x.

Let's start with when x is equal to negative 100.

10 divided by negative 100 gives a solution of negative 0.

1.

Next, if x is equal to negative 20 that means that y is equal to negative 0.

5, or negative 1/2.

Next, if x is equal to negative 10, then y would be negative one.

When x is negative five, y is negative two.

When x is negative, one, y is negative 10.

If x is equal to negative 0.

5, then y to be negative 20.

When we have positive x values, what do you think our y values are going to look like? If x is 0.

5, then y would be 20.

When x is one, y is equal to 10.

When x is equal to five, y is equal to two.

If x is 10, y is one.

When x is 20, y is 0.

5.

And finally, when x is equal to 100, y is equal to 0.

1.

I have drawn the graph of the function, y is equal to 10 over x or 10 divided by x.

You can say that this formed two separate lines.

I've separated my table of values into the negative x values and the positive x values, as these are the two separate graphs.

Here's some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers, x cannot be equal to zero as you can't divide anything by zero.

Here's a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

The curves on each of the sides of the axes should look similar.

Here are some questions for you to try.

Pause the video to complete your task, and resume once you're finished.

Here are the answers.

The y values are the same as for the graph y is equal to one over x, that had been multiplied by negative one.

Here's a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

This is the y equals 1/x graph reflected in the x or y-axis.

Here's a question for you to try.

Pause the video to complete your task, and resume once you're finished.

Here are the answers.

The numerator in this equation is bigger than in the previous questions.

This means that the curves on the graph don't get as close to the origin as two divided by one is two.

Here are some questions for you to try.

Pause the video to complete your task, and resume once you're finished.

Here are the answers.

Graph A does not show a reciprocal graph, and graph C shows a negative reciprocal graph.

So the answer must be B.

That's all for this lesson.

Thanks for watching.