Cubic, Quartic, Reciprocal graphs

when calculating the area of a shape on a graph, what units are used?

units²

cubic graphs - how to find the roots?

(x-1)(x-2)(x-3) —> the roots would be 1,2,3

cubic graphs - what does (x-a)²_mean?

repeated root of a

cubic graphs - what does (x-a)³ mean?

inflection point at a

shape of a cubic graph:

shape of a quartic graph:

what would (x-a)⁴ look like?

touch point (like quadratic)

shape of a reciprocal graph:

define asymptote

a line which the graph approaches but never reaches

for the graph a/x, what would be the asymptotes for x and y?

x=0 y=0

what would the graph of 1/x² look like?

what would the graph 3/x look like compared to 1/x?

the y value would be 3 times greater

what does a change inside the function dictate?

acts on the x-axis, opposite change

what does a change outside the function dictate?

acts on the y-axis, expected change

what does the transformation -f(x) dictate?

reflection in the x-axis

what does the transformation f(-x) dictate?

reflection in the y-axis