Coordinate Geometry, Graphs and Circles (C4)

Question 1

How do you find the equation of a straight line when given two sets of coordinates on the line?

Answer 1

1) Find the gradient (m) using: m=(y2-y1)/(x2-x1)
2) Then plug the m value and coordinat evalues into:
y-y1 = m(x-x1) and rearrange.

OR

1) Find the gradient in the same way.
2) Plug this and the x and y values into y = mx + c and rearrange to find c.

Question 2

How do you find the equation of a straight line when given a set of coordinates and the gradient of a line?

Answer 2

1) Put the gradient, x and y into y-y1 = m(x-x1).

2) Rearrange this into ax+by+c=0

Question 3

How can you tell if a function is a reciprocal function?

Answer 3

They are in the form y=k/x^n or the form y=kx^-n

Question 4

What can you tell about graph of a reciprocal function from its function?

Answer 4

When n in y=k/x^n or y=kx^-n is EVEN :

1) You get a graph of two lines next to each other.
2) If k is POSITIVE both parts of the graph are above the x axis.
3) If k is NEGATIVE both parts of the graph are below the x axis.

When n in y=k/x^n or y=kx^-n is ODD:

1) You get a graph with the two lines opposite each other.
2) If k is POSITIVE the graph is in the top right and bottom left quadrants.
3) If k is NEGATIVE the graph is in the top left and bottom right quadrants.

Question 5

What does y = f(x) + a do?

Answer 5

Translates the graph in the y direction.
   If a > 0 the graph goes upwards.
   If a < 0 the graph goes downwards.
The column vector is (0)
                                    (a)

Question 6

What does y = f(x+a) do?

Answer 6

Translates the graph in the x direction.
    If a > 0 the graph goes to the left.
    If a < 0 the graph goes to the right.
The column vector is (-a)
                                    (0)

Question 7

What does af(x) do ?

Answer 7

Stretches the graph vertically by a scale factor of a.
If a > 1 or a < -1, the graph is stretched.
If -1 < a < 1, the graph is squashed.

For every point, the x coordinate stays the same and the y coordinate is multiplied by a.

Question 8

What does f(ax) do ?

Answer 8

Stretches the graph horizontally by a scale factor of 1/a.
If a > 1 or a < -1, the graph is squashed.
If -1 < a < 1, the graph is stretched.

For every point, the y coordinate stays the same and the x coordinate is multiplied by 1/a.