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From Flashcardlet > pre calc exam review: short answers > Flashcards

pre calc exam review: short answers Flashcards

0
Q

What kind of symmetry do odd functions have?

A

Rotational about the origin

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1
Q

What is the vertical line test?

A

A way to determine whether the graph of an equation is a function y in terms of x

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2
Q

What kind of symmetry do even functions have?

A

Symmetry over the y axis

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3
Q

What is the equation of a vertical line?

A

X=2 (up and down)

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4
Q

What is the equation for a horizontal line?

A

Y=2 (left to right)

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5
Q

What is the slope of a vertical line?

A

Undefined– cannot have zero in the denominator, example: 3/0

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6
Q

What is the slope of a horizontal line?

A

0, because although you may be moving left or right, you’re not moving up or down, example: 0/3

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7
Q

What is the division algorithm?

A 
F(X) = d (X) q (X) + r (X) 
Dividend = divisor X quotient plus remainder
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8
Q

What is the alternative to the division algorithm?

A

Dividend Remainder
——— = quotient + ———–
Divisor Divisor

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9
Q

When does a function have a minimum?

A

When A > 0

*use -b / 2a

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10
Q

When does a function have a maximum?

A

When A < 0

*use -b / 2a

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11
Q

For odd functions…

What do the left and right do as the leading coefficient is positive?

A

Left goes down and right goes up!

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12
Q

For odd functions…

What do the left and right do as the leading coefficient is negative?

A

Left goes up and right goes down!

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13
Q

For even functions…

What do the left and right do as the leading coefficient is positive?

A

Both go up!

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14
Q

For even functions…

What do the left and right do as the leading coefficient is negative?

A

Both go down!

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15
Q

What are logarithms?

A

The “opposite” of exponentials, just as subtraction is the opposite of addition and division is the opposite of multiplication. Logs “undo” exponentials. Technically speaking, logs are the inverses of exponentials.

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16
Q

What is the common log?

A

The logarithmic function with base 10 is called the common logarithmic function.

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17
Q

What is the natural log?

A

Is denoted by the special symbol ln x, read as “the natural log of x” or “el en of x.” The base is understood to be e.

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18
Q

What’s an inverse?

A

When the X and Y values are switched as well as the domains and ranges

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19
Q

What is the midpoint formula?

A

(X1+x2/2) (y1+y2/2)

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20
Q

Symmetry over the x axis becomes

A

(X, -y)

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21
Q

Symmetry over the y axis becomes

A

(-x, y)

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22
Q

Symmetry about the origin becomes

A

(-x, -y)

23
Q

If a function has X axis symmetry…

A

It fails the vertical line test and isn’t a function unless you only draw half

24
Q

What is the domain?

A

Set of all values possible for the independent variable

25
Q

What is the range?

A

All the values possible for the dependent variable

26
Q

What is standard form of a line?

A

ax + by = c

27
Q

What is slope intercept form?

A

y= mx + b

28
Q

What is point slope form?

A

y - y1= m(x - x1)

29
Q

What is the formula for finding slope?

A

M= y - y1 / x - x1

30
Q

Lines that are parallel have…

A

The same slope

31
Q

Lines that are perpendicular have…

A

The opposite reciprocal as the slope

32
Q

What is a relation?

A

A set of ordered pairs

33
Q

What is the greatest integer function?

A

A step function

34
Q

Horizontal lines are what

A

Constants

35
Q

If the number is outside the x term, it’s moving

A

Up or down

36
Q

If the number is inside with the x term, it’s moving

A

Left or right

37
Q

If h(x) = f(-X) then

A

It’s a reflection over the y axis

38
Q

If h(x) = -f(x) then

A

It’s a reflection over the X axis

39
Q

How do you check if functions are inverses?

A

Composite function, it better equal X

40
Q

What is the standard form of a parabola?

A

f(x) = a ( x - h) ^2 + k

41
Q

What is the image to the y intercept on a parabola?

A

The other point symmetrical to your y intercept on the graph

42
Q

What does the intermediate value theorem say?

A

If a < 0 and b > 0 then there’s an X intercept between them

43
Q

Fundamental theorem of algebra says

A

That the number of the leading coefficients equals the number of solutions
3– one real, two imaginary or all three reals

44
Q

You can only use synthetic division when

A

The divisor is linear

45
Q

When you have a positive number and get all positive numbers, it’s an

A

Upper bound

46
Q

When you have a negative number and get all negative numbers you have a

A

Lower bound

47
Q

What is the standard form of a complex number?

A

a + bi

48
Q

Every complex number has a real part as well as

A

An imaginary part

49
Q

When multiplying and there’s a complex number in the denominator…

A

Multiply by the conjugate

50
Q

What is the rational zero test?

A

P / Q to find the possible answers for synthetic

51
Q

How do you find the vertical asymptote?

A

Whatever makes the denominator zero

52
Q

How do you find the horizontal asymptote?

A
  1. If less, X axis is the asymptote.
  2. If equal, the ratio of the num and den
  3. If greater by one, use long division to find equation that is the slant
  4. If greater by two, it’s parabolic
53
Q

How do you find the X intercepts of rational functions?

A

Set numerator to zero

54
Q

How do you find the y intercepts of a rational function?

A

Plug in 0 for x

55
Q

What is Indeterminant form?

A

0/0

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