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Hi, I'm Mr. Bond.

And in this lesson, we're going to learn about reflections of graphs.

Let's take a look at our first example, we're going to consider a function of x.

f of x is equal to x subtract two, all squared.

We're going to sketch this.

So we'll use a table of values.

Calculating the corresponding values of y for each value of x gives us this.

And this is going to give us a graph when we plot these values, that looks something like this, you'd probably need to plot a few more values for it to look exactly like this.

Now, we're going to consider the function, negative f of x.

We'll use a table of values again.

How will our values of y be different? Well, they'll have the same magnitude, but each one will be negative.

So these will be our new values for y.

And if we plot these points on the same coordinate axes, we'd get this.

So what's the same and what's different? The graph of negative f of x is a reflection in the x axis.

Now let's consider another example.

We're going to compare the sketch of f of negative x with our original function, f of x is equal to x subtract two, all squared.

We'll start again with a table of values.

When we calculate our values for y this time, we need to substitute values of x that are negative one multiplied by the values of x in our table and we'll get values of y by this.

Have a look at the table of values.

What's the same and what's different? Hopefully, you noticed that the values for y are the same, but they appear in the opposite order.

And if we plot these points, we'll get a graph that looks something like this.

Again, what's the same and what's different? Hopefully, you've noticed that our new graph is a reflection in the y axis.

Here is a question for you to try.

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

Here are the answers.

In part a, on the same axis, you needed to sketch the graphs of y is equal to negative f of x and f of negative x.

So negative f of x is a reflection in the x axis.

And it will therefore have the same turning point.

And y is equal to f of negative X is a reflection on the y axis.

And therefore its turning point becomes four, zero.

Here's another question for you to try.

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

Here are the answers.

The original function, y is equal to f of x was plotted in blue.

Hopefully, when you plotted the functions, y is equal to negative two f of x and y is equal to f of negative two x, you've got something similar to what's on the screen.

To do it really accurately, you might have wanted to use some online graphing software.

In part a, you'll have seen that again, we have a reflection in the x axis.

But something else also happens.

Why do you think this is? And in part b, y is equal to f of negative two x is the reflection in the y axis.

But there's also another transformation as well.

Can you guess why this one might have happened? Again, investigating both of these phenomena on online graphing software might help.

That's all for this lesson.

Thanks for watching.