Unit 2 Pre Calculus

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

domain and range tip

Answer 19

what x/y cannot be ex. if theres a jump that x coordinate would be the domain like x cannot equal 8

Question 20

what are the zeroes of a graph

Answer 20

the x coordinates of the x intercepts

Question 21

x and y intercepts

Answer 21

wherever the line intersects for x its where the line with just x ex. (4, 0)
same for y just with y line not x line
ex. (0, 9)

Question 22

what coordinates are increasing and decreasing intervals?

Answer 22

x coordinates

Question 23

What do you do when given something like f(-10) and a graph

Answer 23

that means you look at the graph and find the y coordinate on the line corresponding with x = -10

Question 24

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

Answer 24

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 25

what are the three tests for symmetry?

Answer 25

x axis: if replacing y with -y gets the same equation it is true
y axis: if replacing x with -x gets the same equation it is true
origin: if replacing y with -y and x with -x gets the same equation it it true