Prec Calc s1 final study guide

Question 1

draw on a graph: y = x

Answer 1

a

Question 2

draw on a graph:
y = |x|

Answer 2

b

Question 3

draw on a graph:
y = x^2

Answer 3

c

Question 4

draw on a graph:
y = x^3

Answer 4

d

Question 5

draw on a graph:
y = square root of x

Answer 5

e

Question 6

draw on a graph:
y = cube root of x

Answer 6

f

Question 7

draw on a graph:
y = 1/x

Answer 7

g

Question 8

draw on a graph:
y = 2^x

Answer 8

h

Question 9

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

Answer 9

i

Question 10

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

Answer 10

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

Question 11

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

Answer 11

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

Question 12

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

Answer 12

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

Question 13

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

Answer 13

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

Question 14

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

Answer 14

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

Question 15

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

Answer 15

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

Question 16

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

Answer 16

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

Question 17

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

Answer 17

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

Question 18

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

Answer 18

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

Question 19

what are the zeroes of a graph

Answer 19

the x coordinates of the x intercepts

Question 20

what coordinates are increasing and decreasing intervals?

Answer 20

x coordinates

Question 21

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

Answer 21

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)

Question 22

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?

Answer 22

constant horizontal line
Linear
Quadratic
Cubic
Quartic
Quintic

Question 23

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

Answer 23

A. y axis
B. orgin

Question 24

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

Answer 24

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

Question 25

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

Answer 25

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

Question 26

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

Answer 26

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

Question 27

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

Answer 27

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

Question 28

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

Answer 28

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

Question 29

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

Answer 29

a. tangent
b. cross

Question 30

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) = ?

Answer 30

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

Question 31

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

Answer 31

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

Question 32

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

Answer 32

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

Question 33

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

Answer 33

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

Question 34

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

Answer 34

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)

Question 35

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

Answer 35

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

Question 36

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

Answer 36

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

Question 37

What is always the same for Exponential growth and decay?

Answer 37

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

Question 38

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

Answer 38

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)

Question 39

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

Answer 39

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

Question 40

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

Answer 40

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

Question 41

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

Answer 41

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

Question 42

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

Answer 42

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

Question 43

What is the equation for continuously compounded interest?

Answer 43

A = pe^rt

Question 44

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

Answer 44

a. 0
b. 1

Question 45

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

Answer 45

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

Question 46

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

Answer 46

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

Question 47

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

Answer 47

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

Question 48

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

Answer 48

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