Prec Calc s1 final study guide Flashcards by Maren Fricke

draw on a graph: y = x

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draw on a graph:
y = |x|

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draw on a graph:
y = x^2

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draw on a graph:
y = x^3

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draw on a graph:
y = square root of x

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draw on a graph:
y = cube root of x

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draw on a graph:
y = 1/x

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draw on a graph:
y = 2^x

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draw on a graph:
y = [[x]]

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Show graph a
For y = x What is the
a) domain
b) range
c) x intercept
d) y intercept
e) extrema
f) increasing intervals
g) decreasing intervals
h) end behavior
I) discontinuities
j) is it even or odd?
HAS TO BE ABLE TO POINT OUT WHY ON GRAPH

a) all real numbers or (negative infinity to positive infinity)
b) all real numbers or (negative infinity to positive infinity)
c) 0,0
d) 0,0
e) none
f) (negative infinity to positive infinity)
g) none
h)as x ->infinity, f(x) = infinity
as x -> negative infinity, f(x) = negative infinity
I) none
j) odd

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Show graph b
For y = |x| What is the
a) domain
b) range
c) x intercept
d) y intercept
e) extrema
f) increasing intervals
g) decreasing intervals
h) end behavior
I) discontinuities
j) is it even or odd?
HAS TO BE ABLE TO POINT OUT WHY ON GRAPH

a) all real numbers or (negative infinity to positive infinity)
b) y ≥ 0
c) (0,0)
d) (0,0)
e) absolute minimum (0,0)
f) (0, infinity)
g) (negative infinity, 0)
h) as x -> infinity, f(x) = infinity
as x -> negative infinity, f(x) = infinity
I) none
j) even

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Show graph c
For y = x^2 What is the
a) domain
b) range
c) x intercept
d) y intercept
e) extrema
f) increasing intervals
g) decreasing intervals
h) end behavior
I) discontinuities
j) is it even or odd?
HAS TO BE ABLE TO POINT OUT WHY ON GRAPH

a) (negative infinity, positive infinity)
b) y≥0
c) (0,0)
d) (0, 0)
e) absolute minimum (0,0)
f) (0, infinity)
g) (negative infinity, 0)
h) as x -> infinity, f(x) = infinity
as x -> negative infinity, f(x) = infinity
I) none
j) even

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Show graph d
For y = x ^3 What is the
a) domain
b) range
c) x intercept
d) y intercept
e) extrema
f) increasing intervals
g) decreasing intervals
h) end behavior
I) discontinuities
j) is it even or odd?
HAS TO BE ABLE TO POINT OUT WHY ON GRAPH

a) all real numbers
b) all real numbers
c) (0,0)
d) (0,0)
e) none
f) (negative infinity to positive infinity)
g) never
h) as x -> infinity, f(x) = infinity
as x -> negative infinity, f(x) = negative infinity
I) none
j) odd

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Show graph e
For y = square root of x What is the
a) domain
b) range
c) x intercept
d) y intercept
e) extrema
f) increasing intervals
g) decreasing intervals
h) end behavior
I) discontinuities
j) is it even or odd?
HAS TO BE ABLE TO POINT OUT WHY ON GRAPH

a) x≥0
b) y≥0
c)(0,0)
d)(0,0)
e) absolute minimum (0,0)
f) (0, infinity)
g) none
h)as x -> infinity, f(x) = infinity
as x -> negative infinity), f(x) = 0
I) none
j) neither

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Show graph f
For y = cubed root of x What is the
a) domain
b) range
c) x intercept
d) y intercept
e) extrema
f) increasing intervals
g) decreasing intervals
h) end behavior
I) discontinuities
j) is it even or odd?
HAS TO BE ABLE TO POINT OUT WHY ON GRAPH

a) all real numbers
b) all real numbers
c) (0,0)
d) (0,0)
e) none
f) (negative infinity, infinity)
g) never
h) as x -> infinity, f(x) = infinity
as x -> negative infinity, f(x) = negative infinity
I) none
j) odd

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Show graph g
For y = 1/x What is the
a) domain
b) range
c) x intercept
d) y intercept
e) extrema
f) increasing intervals
g) decreasing intervals
h) end behavior
I) discontinuities
j) is it even or odd?
HAS TO BE ABLE TO POINT OUT WHY ON GRAPH

a) x can not equal 0
b) y can not equal 0
c) none
d) none
e) none
f) none
g)
(negative infinity, 0)U(0, infinity)
h)as x -> infinity, f(x) = 0
as x -> negative infinity, f(x) = 0
I) infinite
j) odd

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Show graph h
For y = 2^x What is the
a) domain
b) range
c) x intercept
d) y intercept
e) extrema
f) increasing intervals
g) decreasing intervals
h) end behavior
I) discontinuities
j) is it even or odd?
HAS TO BE ABLE TO POINT OUT WHY ON GRAPH

a) all real numbers
b) y>0
c) none
d)(0, 1)
e) none
f) (negative infinity, positive infinity)
g) none
h) as x -> infinity, f(x) = infinity
as x -> negative infinity, f(x) = 0
I) none
j) neither

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Show graph i
For y = [[x]] What is the
a) domain
b) range
c) x intercept
d) y intercept
e) extrema
f) increasing intervals
g) decreasing intervals
h) end behavior
I) discontinuities
j) is it even or odd?
HAS TO BE ABLE TO POINT OUT WHY ON GRAPH

a) all real numbers
b) all integers
c) (a, 0)
d) (0,0)
e) none
f) none
g) none
h) as x -> infinity, f(x)= infinity
as x -> negative infinity, f(x) = negative infinity
I) yes, wherever a is an integer
j) neither

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what are the zeroes of a graph

the x coordinates of the x intercepts

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what coordinates are increasing and decreasing intervals?

x coordinates

How would you find the rate of change for [1, 2]

those are both x coordinates so you could look at the graph to see the corresponding y coordinates and then use slope equation (y2-y1/x2-x1)

f(x) = c is called and looks like what?
f(x) = x is called what?
f(x) = x^2 is called what?
f(x) = x^3 is called what?
f(x) = x^4 is called what?
f(x) = x^5 is called what?

constant horizontal line
Linear
Quadratic
Cubic
Quartic
Quintic

A. If a function has an even power then it has symmetry with respect to the
B. And if it has an odd power then it has symmetry with respect to the

A. y axis
B. orgin

a. What does it mean if the lead coefficient is positive?
b. and negative?
c. What is this used for most commonly?

a. If positive the right most end goes up
b. If negative the right most end goes down
c. Sketching graphs and end behavior THIS APPLYS TO POLYNOMIAL FUNCTIONS TOO

a. What does it mean if the power is even? b. and odd? c. What is this used for most commonly?

a. Even the left end goes in the same direction as the right one b. Odd the left most end goes in the opposite direction as the right most one c. Sketching graphs and end behavior THIS APPLYS TO POLYNOMIAL FUNCTIONS TOO

What does f(x) = x^-1 equal What does this graph look like

1/x Its the two L looking things that never touch the x or y axis

a. when you have a thing that looks like f(x) = x^n/m what does it also look like? b. If n is even what is the domain? c. If its odd? REMEMBER THESE RULES ONLY APPLY TO PROBLEMS LIKE THIS

a. nth root of x ^m for ex it would be x^3/2 -> the cubed root of x^2 b. x is greater then or equal to 0 c. if odd both range and domain are all real numbers

For Polynomial Functions finding out Domain and Range A. What is Domain? b. If degree is even what is R c. if its odd what is R

a. its always all real numbers b. if the leading coefficient is pos then its y is greater then or equal to … if the leading coefficient is negative then its y is less then or equal to … c. all real numbers

a. For multiplicity if it’s even what does that mean? b. if its odd?

a. tangent b. cross

For Remainder theorem (or synthetic substitution) a. if c= -3 what do you put in the box? b. so you are dividing by c = -3 using synthetic division how do you know what f(-3) = ?

a. -3 b. it equals the remainder which is whatever is in the last column

For Factor theorem how do you determine which binomials are factors of the given function?

you use synthetic division to divide the function by each of the binomials given, they are factors if the remainder is 0. You know the remainder is 0 if you get 0 in the last column THERE CAN BE MORE THEN ONE ANSWER

How do you find the possible rational zeroes of this equation?: x^3-21x+20

do all factors of 20 as numerator and all factors of 1 as denominator each of those are a possible zero then use synthetic substitution to find if its an actual zero or not

given the equation 2x-4/x + 1 with p(x) representing the numerator and q(x) representing the denominator how do you find the a. domain and range? b. x and y intercepts c. holes

a. you find the domain by knowing what makes the denominator 0, the range depends on the equation and if you have a horizontal asymptote is can be that b. for x you use the simplified version of the equation and set p(x)=0 for y you can use either the simplified or non-simplified version of the equation, and you set x=0 its also called f(0) c. There are only holes if there is/are common factor(s) and even then only if you can cancel out all of said common factors. you find the x coordinate by using the non-simplified version of the equation and seeing what makes the denominator = 0 to find the y coordinate substitute the x coordinate number into the simplified version of the equation and what that equals is the y coordinate

given the equation 2x-4/x + 1 with p(x) representing the numerator and q(x) representing the denominator how do you find the a. Horizontal asymptote b. Vertical asymptote c. Slant asymptote d. How do you graph y = mx + b

a. if the degree of p > degree of q there is not HA. if the degree of p < degree of q the asymptote is at y=0 If the degree of p is = degree of q then you find the horizontal asymptote by dividing the leading coefficient of p by the leading coefficient of q b. in the simplified version of the equation set the denominator = 0 c. You can only have a SA if there is no HA and the degree of p has to be exactly one more that the degree off q if this is all true you find it by dividing p(x) by q(x) using synthetic or long division and ignoring the remainder (it should look like y = mx + b d. m is the slope and b is the y intercept (remember rise over run)

How do you know if a function is increasing and called an exponential growth

when a >0 and b>1 ex. f(x) = 2^x

How do you know if a function is decreasing and called an exponential decay

when a >0 and 0

What is always the same for Exponential growth and decay?

D: all real numbers R: y>o Y intercept: (0,1) asymptote: y=0

Transformation rules: a. f(x+h) b. f(x-h) c. f(x) + k d. f(x) -k e-f(x) f. f(-x) g. for transformations like 2(x-3) + 4 what does two do/what is it h. how do you graph 2(x-3) + 4

a. shifts left b. shifts right c. shifts up d. shifts down e. reflects over the x axis f. reflects over the y axis g. 2 stretches/shrinks the graph it functions as the slope (ries over run so up to over 1) h. You start at the origin and go to the right 3 and up 4 and use that point as your new origin then use 2 as your slope (plug in numbers if your confused)

What is the exponential growth and decay function equation? And what do all of the variables mean?

growth: f(t) = a(1+r)^t decay: f(t) = a(1-r)^t a is the initial amount, r is the growth or decay rate (as a decimal) and t is the length of time

What is the continuous growth and decay function? And what do all the variables mean?

A=P(1+r)^t changes to A=P(1-r)^t for decay p is inital amount r is rate t is time

What is the compound interest equation? and what do all the variables mean?

A=P(1+(r/n))^(nt) A is the final/total amount P is the starting amount r is the rate as a decimal n is the number of times compounded per year t is the time in years

For compound interest what are the different numbers n can be? a. weekly b. biannual/semiannually c. bimonthly d. monthly e. quarterly f. daily

a. 52 b. 2 c. 24 d. 12 e. 4 f. 365

What is the equation for continuously compounded interest?

A = pe^rt

Basic properties of Logarithms a. log(subscript b) 1 = ? b log (subscript b) b =?

a. 0 b. 1

for problems like f(x) = 3^x what are the things we know? b>1

D: all real numbers R: y>0 y intercept: (0, 1) Asymptote: y =0 increasing interval: (-infinity, infinity) decreasing interval: none End behavior: as x -> infinity, f(x) -> infinity as x -> - infinity, f(x) -> 0

For problems like f(x) = 1/2 ^x what are the things we know? 0

D: all real numbers R: y>0 Y int: (0,1) Asymptote: y=0 Inc interval: none Dec interval: (-infinity, infinity) End behavior: as x -> infinity, f(x) -> 0 as x -> - infinity, f(x) -> infinity

For problems like f(x) = log (subscript 3) x what are the things we know? b > 1

D: x>o R: all real numbers x int: (1,0) Asymptote: x = 0 Inc interval: 0, infinity Dec interval: none End behavior: as x -> infinity, f(x) -> infinity as x -> 0, f(x) -> -infinity

For problems like f(x)= log (subscript 1/2) x what are the things we know? 0

D: x>0 R: all real numbers x int: (1, 0) Asymptote: x = 0 Inc interval: none Dec interval 0, infinity End behavior: as x -> infinity, f(x) -> -infinity as x -> 0, f(x) -> infinity