# Grade A* Facts to memorise

What does the graph of y = sinθ look like?

What does a cos graph look like?

What does a tan graph look like?

What does the graph of y = f(x) + n look like?

eg if f(x) = x^{2}, then y = x^{2} + n

What does the graph of y = f(x) - n look like?

eg if f(x) = x^{2}, then y = x^{2} - n

What does the graph of y = f(x + n) look like?

eg if f(x) = x^{2}, then y = (x + n)^{2}

What does the graph of y = f(x - n) look like?

eg if f(x) = x^{2}, then y = (x - n)^{2}

What does the graph of y = nf(x) look like?

eg if f(x) = x^{2}, then y = nx^{2}

What does the graph of y = f(nx) look like?

eg if f(x) = x^{2}, then y = (nx)^{2}

What does the graph of y = f(x)/n look like?

eg if f(x) = x^{2}, then y = x^{2}/n

What does the graph of y = f(x/n) look like?

eg if f(x) = x^{2}, then y = (x/n)^{2}

What is the formula for a circle?

What is the CAST diagram?

Graph moves n places upwards.

Graph moves n places downwards.

Graph move n places to the left

Graph moves n places to the right

Graph is stretched up/down by a factor of n

The graph is squashed left/right by a factor of n.

The graph is squashed up/down by a factor of n.

The graph is stretched left/right by a factor of n.

x^{2} + y^{2} = r^{2}

How do you solve the equation f(x) = g(x) using graphs?

- Draw the graphs of y = f(x) and y = g(x)
- The solutions are where the graphs intersect.