CHAPTER 5

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5C Translation

Translations shift or move the graph wthout changing its shape

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for y=f(x)+b, the effect of b is to translate the graph vertically through b units

For y=f(x-a), the effect of a is to translate the graph horizontally through a unit.

For y=f(x-a)+b, the graph is translated horizontally through a units(right), and vertically trough b units(up)
We say it is

5A Graphing function

Modulus： f(x)=|x|

Exponential: f(x)=a^x, a＞0， a≠1

Cubic: f(x) ax^3+bx^2+cx+d, a≠0

Logarithms: f(x)=log10x, b＞0, x＞0

Quadratic: f(x)-ax^2+bx+c, a≠0

Linear: f(x)=ax+b, a≠0

Reciprocal: f(x)=1/x, x≠0

Rational: f(x)=ax+b/cx+d, x≠-d/c

5E Reflection

reflection in an axis change the polarity(sign) of one of the coordinates

for y=-f(x) we reflect y=f(x) in the x-axis

for y=f(-x) we reflect y=f(x) in the y-axis

another special reflection. if we reflect in y=x, we find the inverse

5D streches

Sketches change the shape of a graph by scaling the distance of each point relative to an invariant axis, on which the points do not change position.

For y=pf(x), the effect of p is to vertically stretch the graph by a scale factor p with invariant x-axis

For y=f(qx), the effect of q is to horizontally stretch the graph by a scale factor 1/q with invariant y-axis

5F Miscellaneous Transformation