Pre-Cal D

Front 1

Any set of ordered pairs

Back 1

Relation

Front 2

*A point at which a graph intersects the x-axis

Back 2

X-intercept

Front 3

*A point at which a graph intersects the y-axis

Back 3

Y-intercept

Front 4

*A graph that is unchanged when reflected about the x-axis
(for all)(x,y) E function f, (x,-y) E function f

Back 4

Symmetric wrt x-axis

Front 5

*A graph that is unchanged when reflected about the y-axis.
(for all)(x,y) E function f, (-x,y) E function f

Back 5

Symmetric wrt origin

Front 6

*equations that have the same solutions

Back 6

Equivalent equations

Front 7

*An equation in the form ax^2+bx+c, where a,b and c are constant

Back 7

Quadratic equation

Front 8

*An equation which has a rational expression on one or both sides of the equation

Back 8

Fractional equation

Front 9

A value which is not a decimal approximation

Back 9

Exact value

Front 10

*If a and b are complex numbers, and ab=0, then a=0 or b=0 inclusively

Back 10

Zero-factor property

Front 11

*If a=b, then a+c=b+c

Back 11

Addition property for inequalities

Front 12

*If a=b, then ac=bc

Back 12

Multiplication property for inequalities

Front 13

√[(x(sub 1) – x(sub 2))^2 + (y(sub 1) – y(sub 2))^2] = distance

Back 13

Distance formula

Front 14

([x1+x2]/2,[y1+y2]/2) = midpoint

Back 14

Midpoint formula

Front 15

(x-h)^2 + (y-k)^2 = r^2
center:(h,k), radius:r

Back 15

Circle equation

Front 16

*rise/run
(y2-y1)/(x2-x1)

Back 16

Slope formula

Front 17

*x=a where a is the x-intercept

Back 17

Vertical line equation

Front 18

*y=a where a is the y-intercept

Back 18

Horizontal line equation

Front 19

Point-slope form

Back 19

y – y(sub 1) = m(x – x(sub 1))
m:slope, (x(sub1),y(sub1)) is a point on the line

Front 20

Slope-intercept form

Back 20

y=ax+b
a:slope, b:y-intercept

Front 21

General form (linear equation)

Back 21

Ax + By = C

Front 22

Discriminant

Back 22

*b^2-4ac

Front 23

Domain

Back 23

Set of 1st coordinates of the ordered pairs of a relation

Front 24

Range

Back 24

Set of 2nd coordinates of the ordered pairs of a relation

Front 25

Function

Back 25

Relation in which no 2 ordered pairs have the same 1st coordinate

Front 26

Vertical line test

Back 26

If a vertical line intersects the graph of a relation in more than 1 point, then the relation is not a function

Front 27

Average rate of change

Back 27

[f(b)-f(a)]/[b-a]

Front 28

Increasing on an interval

Back 28

(for all)a,b in the interval with a<b, f(a) < f(b)

Front 29

Decreasing on an interval

Back 29

(for all)a,b in the interval with a<b, f(b) < f(a)

Front 30

Constant on an interval

Back 30

(for all)a,b in the interval, f(a) = f(b)

Front 31

Local maximum

Back 31

function value f(c) for which (there exists)an open interval containing c (such that) (for all)x≠c in the interval, f(c) > f(x)

Front 32

Local minimum

Back 32

function value f(c) for which (there exists)an open interval containing c (such that) (for all)x≠c in the interval, f(x) > f(c)

Front 33

Even function

Back 33

Function f (such that) f(-x)=f(x) (for all)x E Domain of f

Front 34

Odd function

Back 34

Function f (such that) f(-x)=-f(x) (for all)x E Domain of f

Front 35

Sum function

Back 35

2 functions f and g (such that) (f+g)(x)=f(x)+g(x)

Front 36

Difference function

Back 36

2 functions f and g (such that) (f-g)(x)=f(x)-g(x)

Front 37

Product function

Back 37

2 functions f and g (such that) (f*g)(x)=f(x)*g(x)

Front 38

Quotient function

Back 38

2 functions f and g (such that) (f/g)(x)=f(x)/g(x)

Front 39

Composite function

Back 39

2 functions f and g (such that) (f○g)(x)=f(g(x))
Domain of f○g = {x: x E Domain of g AND g(x) E Domain of f}

Front 40

Quadratic function

Back 40

Function of the form f(x)=ax^2+bx+c, a≠0