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15 Cards in this Set

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f(x) + p transforms a function by

translating p units veritcally

pf(x) transforms a function by

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.

f(px) transforms a function by

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.

-f(x)

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

f(-x)

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

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

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

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

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

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

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

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

The opposite order is used: addition, then multiplication.

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

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)





even function test

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

odd function test

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

f(x+p) transforms a function by

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

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

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

to solve equations involving abs of both sides..

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