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Flashcards in Prep for Calculus Deck (52):
1

apex of  y = x2 -2,

opens up, (0, -2)

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

3

 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.

4

 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

5

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

When replacing y with -y yields an equivalent equation

6

Tests for Symmetry, symmetric with respect to the origin

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

7

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

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

8

When a polynominal has symmetry with respect to the origin

when each term has an odd exponent

9

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

When replacing x with -x yields an equivalent equation

10

When is a slope zero?

When is a slope undefined?

Zero when horizontal

Undefined when vertical

11

Point-Slope Form of the Equation of a Line

y -y1= m(x -x1)

12

The Slope-Intercept Form of the Equation of a Line

y=mx+b

13

the equation of any line can be written in the general
form:

Ax+By+C=0

where A and B are both not 0

14

the graph of y=2

  A horizontal line at y=2

15

direction of line for y=-1/3x +2 

sloping down to the right

16

Slope relationship between  two perpendicular lines

m1=-1/m2

17

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

x is the independent variable.

y is the dependent variable.

18

what is the difference between implicit and explicit form equations

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

19

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

and the range

[1,  )

[0,∞ )

20

f(x)=x3

 

21

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

22

f(x)=|x|

23

Rational function

f(x)=(1/x)

24

sine function

f(x)=sin x

25

cosine function

f(x)=cos x

26

Transformations of functions

f(x)=x2

f(x)=x2+C

27

Transformations of functions

  f(x)=x2

 f(x)=(x+1)2

28

  Transformations of Functions

f(x)=x2

f(x)=-x2

29

Transformations of functions

  f(x)=x2

f(x)=(x-2)2+4

30

Transformations to y=f(x)

y=f(x - c)

horizontal shift c units to the right

31

Transformations to y=f(x)

y=f(x + c)

horizontal shift c units to the left

32

Transformations to y=f(x)

y=f(x) - c

vertical shift c units downward

33

Transformations to y=f(x)

f(x) + c

vertical shift c units upward

34

Transformations to y=f(x)

y= -f(x)

Reflection about the x-axis

35

Transformations to y=f(x)

y= f(-x)

reflection about the y-axis

36

Transformations to y=f(x)

y = -f(-x)

reflection about the origin

37

constant function

f(x) = a

38

linear function

f(x) = ax + b

39

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

40

The function y = f(x) is even when

f(-x)  = f(x) 

41

The function y = f(x) is odd when

f(-x) = -f(x)

42

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

43

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. 

44

Exponent Rule

bxby=

bx+y

45

Exponent Rule 

(bx)y

bx*y

46

the solution of 2x=7

x=log2(7)

47

logb(y) in narrative terms

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

48

you can't take the logarithm of ____ or ___

a negative number or 0

49

50

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

horizontal line test

51

The consequence of failing the vertical line test

not a function

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

52