CH4 - Graphs And Transformations

What is a Cubic Graph?

A graph with the function f(x) = ax³ + bx² + cx + d

It can have up to two turning points.

a > 0 , Increasing Graph

a < 0  ,  Decreasing Graph

What is a Quartic Graph?

A graph with the function f(x) = ax⁴ + bx³ + cx² + dx + e

It can have up to three turning points.

a > 0 , Decreases then Increases

a < 0 , Increases then Decreases

What is a Reciprocal Graph?

A graph representing the function f(x) = 1/x, which has vertical and horizontal asymptotes. It reflects the inverse relationship between x and y.

It approaches the axis but never reaches it

What are Points of Intersection?

Points on a graph where lines y = f(x) and y = g(x) become f(x) = g(x)

How do you translate graphs and what are some key transformations?

Translation involves shifting the graph horizontally or vertically.

y = f(x) + a Is a transformation by vector (0/a)

y = f(x + a) Is a transformation by vector (-a/0)

y = af(x) is a stretch of the graph by sf a in the vertical direction

y = f(ax) is a stretch of the graph by sg 1/a n the horizontal direction

y = f(-x) is a reflection across the y-axis

y = -f(x) is a reflection across the x-axis