Lesson video

Hi, I'm Mrs. Dennett.

And in this lesson, we're going to be looking at functions.

In particular, we're going to be looking at a particular value for a function.

I don't think I could have said the word particular any more times there.

Basically, we're going to be doing lots of substitution.

Here, we have a function of f.

We write this as f bracket x, and we say function of x.

The function of x is five x.

This means that x is being multiplied by five.

We want to find the values of the following.

For the first question part a, we can see that the value of x is seven.

So we substitute seven into the function of x, five times seven gives us 35.

For the next question, the value of x is negative two.

So we substitute negative two into the function of x, and five times negative two is equal to negative 10.

In part C, we have a decimal as a value of x.

So we do exactly the same thing, five times 3.

2 which is equal to 16.

We could also have fractions for the value of x.

So we multiply five by 3/5, and this gives us three.

And finally, sometimes we could have a value such as eight x as our value for x.

So the function of eight x would be five times eight x, which is equal to 40 x.

Let's have a look at a different function of x.

Here, the function of x is five times x add two, and we're going to substitute the same values in as before for our functions.

So the first value was x is equal to seven.

So we substitute x is equal to seven into our function, we know that five times seven was 35 and we just add two and we get 37.

Next we substitute in negative two, so we do five times negative two, which is negative 10, and then add two, which is negative eight.

And remember we're moving closer towards zero when we add two to negative 10.

Next we're going to substitute 3.

2 into our function five X plus two.

So we do five times 3.

2, which was 16, and then add two, which gives us 18.

We can do the same for the function of 3/5.

So we put 3/5 into our function.

Five times 3/5 add two is equal to five.

And finally for our function of eight x, we put five times eight x add two, which is 40 x plus two.

Here's some questions for you to try.

Pause the video to complete the task and restart when you're finished.

Here are the answers, oh, quite straightforward really.

Just be careful with the last question, you should be multiplying three by three x.

Here are some questions for you to try.

Pause the video to complete the task and restart when you're finished.

Here are the answers.

Just take care of the last two questions here.

So five times 3/5 is three, and then we subtract three, which gives us zero.

And for part D, you need to expand the bracket.

So five times all of x plus six gives the five x plus 30, and remember to subtract three at the end, giving us five x plus 27.

We're now going to look at the function of x that contains an x squared term in it.

So here we've got a function of x is equal to three x squared takeaway x.

So we have to be very careful here that we multiply the x by itself, we do x squared first and then multiply by three and take away x.

So you can see, I put brackets around the x terms here.

And this just helps us to think about the number that we are substituting into our function.

It's also useful if you're doing this on a calculator, because you can type in the function like this, leave the x parts blank, and then you don't have to keep retyping the function for each part of the question, you can just go back and type in the number the you are substituting in.

So for the first one we're going to substitute in x is equal to seven.

So our function of seven will be three times seven squared take away seven, and that gives us three times 49, remember we do the seven squared first to get 49, times by three and take away seven and that gives us 140.

Now we're going to look at substituting a negative number in to this function, so we're going to do three lots of negative two squared take away negative two.

So this will be negative two squared first, which gives us four, multiply that by three, and then because we're taking away negative two, that's the same as adding, so we're going to do three times four, add two, which gives us 40.

The same is true for substituting decimals in.

So we've substituted a positive number, a negative number, and now we're going to substitute a decimal in.

So we've got 3.

2 into our function, you can see I've just put 3.

2 in the brackets.

And we end up with 27.

52.

We're now going to try a fraction, so we're going to do 3/5 squared first, thinking about our order of operations, squaring a number is more important than multiplying so we do that part first.

So we get 3/5 squared which is 9/25, multiply that by three, take away 3/5, and we get 12/25.

And finally, if you want to substitute eight x into our function of x, we get three lots of eight x squared, so that's three lots of 64 x squared, make sure you multiply the eight by itself and the x by itself to get 64 x squared.

And then we take away eight x, so we end up with 192 x squared take away eight x.

There is a question for you to try.

Pause the video to complete the task and restart when you're finished.

Here are the answers.

For part F, make sure that you square four X first to get 16 x squared, and then times by two to get 32 x squared, Here is a final set of questions for you to try.

Pause the video to complete the task and restart when you're finished.

Here are the answers.

Our function is a quadratic one, so take your time to substitute into this equation carefully, especially with the negative four in part C.

Negative four squared is positive 16, and then we have to take away negative four multiply by negative four.

So essentially, adding on 16 to get 32, and then add three to get 35.

That's all for this lesson.

Remember to take the exit quiz before you leave.

Thank you for watching.