apex of y = x2 -2,

opens up, (0, -2)

A graph is symmetric with respect to the x-axis if,

whenever (x,y) is a point on the

graph, then (x, -y) is also a point on the graph

A graph is symmetric with respect to the origin if,

whenever (x,y) is a point on

the graph, then (-x,-y) is also a point on the graph. This means that the graph is

unchanged by a rotation of 180º about the origin.

A graph is symmetric with respect to the y-axis if,

whenever (x,y) is a point on the

graph, then (-x,y) is also a point on the graph

Tests for Symmetry, symmetric with respect to the x-axis

When replacing y with -y yields an equivalent equation

Tests for Symmetry, symmetric with respect to the origin

When replacing x with -x, and y with -y, yields an equivalent equation

When a polynominal has symmetry with respect to the y-axis

when each term has an even exponent (or is a constant).

When a polynominal has symmetry with respect to the origin

when each term has an odd exponent

Tests for Symmetry, symmetric with respect to the y-axis

When replacing x with -x yields an equivalent equation

When is a slope zero?

When is a slope undefined?

Zero when horizontal

Undefined when vertical

Point-Slope Form of the Equation of a Line

y -y_{1}= m(x -x_{1})

The Slope-Intercept Form of the Equation of a Line

y=mx+b

the equation of any line can be written in the general

form:

Ax+By+C=0

where A and B are both not 0

the graph of y=2

A horizontal line at y=2

direction of line for y=-1/3x +2

sloping down to the right

Slope relationship between two perpendicular lines

m_{1}=-1/m_{2}

x and y in a function. what are x and y called?

x is the independent variable.

y is the dependent variable.

what is the difference between implicit and explicit form equations

y is isolated by itself on one side of the equation in explicit form

How to write the domain for f (x)=(x-1)^(1/2)

and the range

[1, ∞ )

[0,∞ )

f(x)=x^{3}

f(x)=x^(1/2)

f(x)=|x|

Rational function

f(x)=(1/x)

sine function

f(x)=sin x

cosine function

f(x)=cos x

Transformations of functions

f(x)=x^{2}

f(x)=x^{2}+C

Transformations of functions

f(x)=x^{2}

f(x)=(x+1)^{2}

Transformations of Functions

f(x)=x^{2}

f(x)=-x^{2}

Transformations of functions

*f*(x)=x2

*f*(x)=(x-2)^{2}+4

Transformations to y=*f*(x)

y=*f*(x - c)

horizontal shift c units to the right

Transformations to y=*f*(x)

y=*f*(x + c)

horizontal shift c units to the left

Transformations to y=*f*(x)

y=*f*(x) - c

vertical shift c units downward

Transformations to y=*f*(x)

*f*(x) + c

vertical shift c units upward

Transformations to y=*f*(x)

y= -*f*(x)

Reflection about the x-axis

Transformations to y=*f*(x)

y=* f*(-x)

reflection about the y-axis

Transformations to y=*f*(x)

y = -*f*(-x)

reflection about the origin

constant function

*f*(x) = a

linear function

f(x) = ax + b

a function* f *is

rational when it has the form:

*f *(x) = *p*(x)/*q(*x)

*where q*(x) does not equal 0

and *p*(x)/*q*(x) are polynominals

The function y = *f*(x) is **even** when

*f*(-x) = *f*(x)

The function y =* f*(x) is odd when

*f*(-x) = -*f*(x)

least squares regression

equation to represent data

the closer the correlation coefficient, r, is to 1, the better the data can be modeled by a line.

If r is positive, then variables have positive correlation, if negative, then variables have a negative correlation

what is the difference between the codomain and the range?

The range is a subset of the codomain. The codomain is a set of all possible outputs, while the range is the set of actual outputs.

Exponent Rule

b^{x}b^{y}=

b^{x+y}

Exponent Rule

(b^{x})^{y}

b^{x*y}

the solution of 2^{x}=7

x=log_{2}(7)

log_{b}(y) in narrative terms

the power you have to raise the base b in order to get y

you can't take the logarithm of ____ or ___

a negative number or 0

The test a function must pass to determine it has an inverse

horizontal line test

The consequence of failing the vertical line test

not a function

for every x value, you must have only one corresponding y value