00:01
In this question, we're going to be selecting all the statements that are true for the function g of x, which equals negative 3, f of x plus 4 minus 2.
00:15
Now, when we look at g of x, now let's look at all these sentences first of all, the sentences where we do not have to evaluate anything.
00:26
Now, f of x, let's start from that one.
00:29
F of x is stretched vertically by a factor of 3.
00:34
Is that true or false? that's a true statement because looking at the coefficient of f of x we notice that the coefficient is 3.
00:49
So that tells us that we are going to be stretching by a scale factor of 3.
00:55
So this is true.
00:58
Next, we have f of x is shifted down two units.
01:05
Yes, that's true because you're subtracting two.
01:10
Next, f of x is compressed vertically by a scale factor of negative 3.
01:16
Now this is not so correct, it's not compressed because for it to be compressed, the coefficient should be a fraction.
01:25
So this is wrong.
01:27
And f of x is shifted four units to the right so when we see x plus four it means that we need to move four steps to the right to get to the origin so that means it has been shifted four units the left so this is wrong next f of x is reflected horizontally now the way we can tell whether it's a reflection horizontal reflection is we're looking at the sign of the coefficient at the beginning so the coefficient at the beginning is negative so that means that we are reflecting around the x -axis so that's a vertical reflection not a horizontal reflection so the correct one is x is reflected vertically and not horizontally.
02:36
Next, we want to work out some of these values here.
02:42
If you are given that f of x is negative, 2x squared plus 5, that's appearing two times in this option and this option.
02:54
And also, given that f of x is 2x squared, it's given two times there.
02:59
So we need to work this, work this out.
03:01
So if f of x is 2x squared, so what will this function be? now g of x will be equal to negative 3.
03:17
Now remember f of x is, let me just rewrite this.
03:24
F of x is 2x squared.
03:33
So what would f of x plus 4p? be 2 in brackets x plus 4 squared and that's what i should put right after negative 3.
03:52
So right after negative 3 i should have 2 in brackets x plus 4 squared and then we close up bracket minus 2.
04:05
So we want to check whether that is what follows from here.
04:13
When we simplify this is going to be g of x equals negative 6 and then brackets x plus 4 squared minus 2...