Ib Hl Math 6

Front 1

f(x) + p transforms a function by

Back 1

translating p units veritcally

Front 2

pf(x) transforms a function by

Back 2

The graph is stretched by a factor of p vertically. If abs(p)<1, the graph is compressed towards the x axis. If p<0, the graph is reflected over the x axis and then stretched by a positive factor.

Front 3

f(px) transforms a function by

Back 3

The graph is compressed by a factor p to the y axis or stretched by a factor of 1/p. Note that if p is negative, the result will be a version of the graph reflected over the y axis and then compressed by a positive factor.

Front 4

-f(x)

Back 4

f(x) is reflected over the x axis to become -f(x).

Front 5

f(-x)

Back 5

f(x) is reflected over the y axis to become f(-x).

Front 6

f(x) transformed to abs(f(x)) by

Back 6

For any part of the graph with y values less than 0, this section is reflected over the x axis.

Front 7

f(x) transformed to f(abs(x)) by

Back 7

Remove any points with x<0 from the graph, and add a reflection over the y axis of the remaining portion to the graph.

This can be done because now f(-x)=f(x), so these y values are the same

Front 8

With vertical transformations, (outside transformations) the order of transformations is

Back 8

The same order of operations used in arithmetic: multiplication, then addition.

Front 9

With horizontal transformations, (inside transformations) the order of transformations is

Back 9

The opposite order is used: addition, then multiplication.

Front 10

What happens to f(x) when you transform it to 1/f(x)?

Back 10

Any roots become vertical asymptotes, and vertical asymptotes become roots. Any tendencies towards infinity become tendencies to 0 from above, and the opposite for negative infinity (maximums become minimums and vice versa). Pay particular attention to the values of maxima and minima and y-intercepts. These will all become 1/f(x)

Front 11

even function test

Back 11

For an even function, f(x)=f(-x).

Front 12

odd function test

Back 12

For an odd function, -f(x)=f(-x).

Front 13

f(x+p) transforms a function by

Back 13

translating -p units horizontally (if positive p to the left, if negative p then to the right)

Front 14

to solve equations involving the abs of one side...

Back 14

solve two equations, one for the positive result and one for the negative

Front 15

to solve equations involving abs of both sides..

Back 15

make a quick sketch and determine which of the positive and negative forms of each respective side are intersecting