Math Investigation
Transformation of graphs
A.1:By looking at the different graphs we can observe the effects of k in the function. In the graphs acts on the y-axis, by the changing the value of k the y axis goes down or up, it’s a vertical translation. When the value is positive the parabola goes up and when is negative it goes down. In the first graph when K is 4 it moves four spaces up in the y axis and the second one when K is -3 it moves three spaces down. Although the line moves the curve is not affected, this means that the gradient is not affected.
A.2:

My observations from last exercise apply to this graphs. The value of k is still a constant so the line keeps moving the y axis upwards or downwards depending on the value , it doesn’t move through the x axis , this means that the gradient never changes.
A.3:Generalisation
When ever the value of K is a constant it will only affect the line on the y axis .Theres a vertical translation on the line, when the value is positive it moves upwards and when is negative it moves dowards from the original line.The cruve of the line never changes this in other words mean that the gradient stays the same and the line don’t moves through the x axis.
B.1

By looking at the graphs above we can observe the effects of h on the function. On the first graph the value of his 3 so it moves to the right three spaces.There is a horizontal translation on the x axis.If the values I positive it moves to the right and if negative it moves to the left.
B.2

. This is because it affects in the same ways due to the fact that they both are moving along the x-axis therefore making a horizontal translation. There is no change in the y intercept when the value of k is changed.
B:3
If h is positive the line of the graph moves to the right and if h is negative the line of the graph movesthe left in the same axis, making a horizontal translation of which means thatthe line will move h spaces in the x-direction and 0 spaces in the y-direction. Gradient allways remains the same.
C:1
You can see clearly in the graph that there are two transformations on the original line to the one in blue. There is a vertical and horizontal and vertical translation, first there is 5 moves to the right in the x axis and then a move up in the y axis 4 spaces.
C:2The graph will first translate h units in the x-direction, as h is negativegraph will move to the right, doing a horizontal translation. After this, it will also translate k units in the y-direction, as k is positive graph will move upwarDdoing a vertical translation. We will also observe that the graph moved.
D.1

By looking at the graphs we can see the effects of a in the line.On the first graph we can see that the curve stretched compare to the original line.The bigger the value of A the most it stretches.But when the value of A is negative the line turns upside down.

D.2

When the value a is negative it goes upside down and the greater the value the more its strectches.You can see it clearly in the graphs with the values for a of 4,2and-2.
D.3
Whenever we have a function that we know A is a constant in the line of x in the absolute value now know that when the value of A is negative the line is going to turn upside down.And that the line when greater the value there is a vertical stretch.It only affects the y coordinates.
E.
F.

In the graph above you can see the vertical and horizontal transformation made.First there is a move of 4 spaces to the right on the x axis then it moves 3 spaces down on the y axis.And the last transformation is a reflection on the x axis.
F.2

G.1

The constant a poduces a horizontal stretch on the function . On the first graph the value of a is 0.3, this means that the graph stretched in a scale factor . We may notice that when the values of a are 0< a <1, the curve is further apart from the y-axis and the x -intercepts are greater than -1 and 1. When the values for a are a <1, the curve is near the y-axis, the greater the value for a the much closer to the y-axis the curve will G.2

We can see that a affects in the same ways due to the fact that in both excercises they are stretching horizontally in the -axis.. If a is 0< a <1 the curve will have less frequency. When the values for a are a <1 the curve will have more frequency, the grater the value for a the more frequency the curve will have and the smaller the values for a the less frequency the curve will have. The a once again determines that the scale factor will be. The y-coordinates do not change. Generalisation G.3 We know that a is the constant.It stretches horizontally, this is, a stretch parallel to the -axis with a scale factor of . If a is 0< a <1 the curve will be further apart from the y-axis compared to original function. When the values for a are a <1 the curve is closest to the y-axis, the grater the value for a the closest to the y-axis the curve will be. The only values affected are the -coordenates. H. My function used is f(x)=x ^2 .And you can see clearly in the the graphs f(-x).There is a reflection in the x axis.It turns upside down.