Functions- lecture video

Question 1

How many outcomes can a function have

Answer 1

one
each input determines one unique output

Question 2

What is the Domain

Answer 2

x value or input value or independent variable

Question 3

what is the range

Answer 3

y value or output value or dependent variable

Question 4

What test can we use to determine if a graph is a function

Answer 4

vertical line test
- the vertical line can only pass through one co-ordinate

Question 5

is this a function? Why or why not
X^2 + y^2 = 25

Answer 5

no, we need to
at 15:15 add more
but you end up with more than one answer +/_ so it is not a function

Question 6

What is important about graphing piecewise functions

Answer 6

by graphing each piece individually

Question 7

What are the restrictions for A=S^2

Answer 7

S must be greater than or = to zero
(cannot be a negative number)

Question 8

what are the restrictions for y = 1/ x

Answer 8

x cannot = 0

0 would make it undefined

Question 9

what are the restrictions for F(x) = the square root of x

Answer 9

x must be greater than or = to zero

Question 10

what are the restrictions for f(x) = x ^3

Answer 10

no restrictions, so the domain is all real numbers

Question 11

what are the restrictions for f(x) = 1 / (x-1) (x-3)

Answer 11

X is all really numbers except x cannot = 1 or 3

Question 12

What happens if you cannot simplify restrictions out of your functions

Answer 12

these will be vertical asymptotes

Question 13

What are the restrictions for f(x) = Tan x

Answer 13

(an s shape for tangents, because it is undefined at certain points)

= sin x / cos x
therefore, cos x cannot = 0

x cannot = pi/ 2
x cannot = 3 pi / 2
etc

Question 14

what are the restrictions for f(x) = square root (x^2-5x +6)

Answer 14

1. if you have a square root, the numbers must be positive in it
2. we know that (x^2 - 5x + 6 must be greater than or = to zero)
3. We need to factor this question because it is a quadratic equation

= (x - 3)(x-2) is greater than or = 0

this is an inequality, becareful, it’s not 3 and 2

4. so we know x = 2 and x = 3 are important points, make a number line and put the points on the number line then do a test
5. here we plug in 0 (to the left of 2) into the equation, you get positive 6
   - every number to the left of 2, will be a positive number
6. try a point greater than 3, we plug in 4 and we get a positive number
7. try a point b/w 2 and 3, we choose 2.5 and we get a negative number

Therfore the domain is:
(- infinity,2]U [3, + infinity)

Question 15

Big thing with restrictions is

Answer 15

look for
1. denominators
- the bottom cannot = 0

2. roots
   - cannot use negative numbers as the answer

Question 16

What are the restrictions for f (x) = x^2 - 4 / x-2

Answer 16

1. we know the denominator cannot be 0 however, we can factor this
2. factor this out we get
   (x+2) (x-2) /x-2
   - we can now cancel out the two x-2s and we get
   x+2
3. so the domain is all real numbers except we still have to keep the original domain restriction that x cannot = 2

Question 17

If the restriction is x cannot = 2 what also can we say about x = 2 on the graph

Answer 17

we have a point on the graph not filled in or a hole

or a removable discontinuity (or not continuous graph)

Question 18

If you can cancel out your domain problem (ie. the denominator can be cancelled out by factoring) then you have what

Answer 18

a hole

Question 19

If you cannot cancel out your domain problem (ie. the denominator by factoring) what is it

Answer 19

an asymptote

Question 20

What are the restrictions for 3x / x-4

do you have a hole or asymptote

Answer 20

1. x cannot = 4
2. we cannot factor the denominator out so we have a vertical asymptote

Question 21

what are the restrictions for
f(x) = 2 + square root of x-1

What is the domain and what is the range

Answer 21

x-1 cannot = be negative or must be greater than or = to zero

so x must be greater than or equal to 1
Domain:
interval
[1, infinity)

Range: [2, infinity)

Question 22

how do you find your range?

Answer 22

plug in your domain (for now, for simple items)

Question 23

what is the domain and range for y = (x+1)/ (x-1)

Answer 23

Domain: x cannot = 1
bc 1 -1 =0 in the denominator

all real numbers except 1

now plug in 1 into the whole equation you get
2/ 0 which is a vertical asymptote

Range: if you solve for y you get
x = y+1 / y-1
y cannot = 1
horizontal asymptote

Question 24

What are even functions

Answer 24

functions that have 2s, 4s, 6s, and 8,s in them etc

Question 25

What are odd functions

Answer 25

functions that have odd numbers in them

Question 26

even functions are symmetric how

Answer 26

symmetric across the y-axis
f(-x) = f(x)

Question 27

odd functions are symmetric how

Answer 27

symmetric about the origin (mirror image)
f(-x) = -f(x)

Question 28

how to test to see if something is even

If f(x) = x^4 - x^2+1

Answer 28

plug in negative x and see what happens
f(-x) = (-x)^4 - (-x)^2+1
becomes…

x^4-x^2+1 - we got back the same thing!

THis means it is an EVEN function

Question 29

is it even or odd function

f(x) = x^3 - x

Answer 29

to figure out, plug in -x

f(-x) = (-x)^3 - (-X)
becomes….

F(-x)= -x^3 +1

We got the opposite back so this means it is

an ODD Function