Graphs

Question 1

What do we need to draw a decent graph

Answer 1

Points of intersect with x and y axis, asymptotes and stationary points.
Domain and range

Question 2

Finding intersection with y axis

Answer 2

Set x = 0 may need to find a limit

Question 3

Finding intersection with x axis

Answer 3

set y = 0 likely have to solve a quadratic or higher: use long algebraic division

Question 4

Finding asymptotes

Answer 4

Find value at infinity or values of discontinuity (potential vertical asymptotes

Question 5

Finding stationary points

Answer 5

Occur when f’(x) = 0

Question 6

Determining nature of stationary points

Answer 6

Use 2nd order or higher derivatives of the function at our desired points.
For n where f^n(x)=0 and f^(n+1)(x) ≠ 0
If n is odd: <0 max, >0 min
If n is even: < 0 decreasing inflection, >0 increasing inflections

Question 7

Domain and range

Answer 7

Can be determined from previously but draw them in graph

Question 8

What does a stationary point of inflection look like

Answer 8

A point where gradient = 0 but the ‘direction’ doesn’t invert