Question

Using complete sentences, prove to Splott and Fizzle that your function is a legitimate function

Answer 1

here is my function

f(x)=6x+2
f(4)=f(4)+2=24+2=26

Answer 2

@zepdrix

Answer 3

@phi

Answer 4

the first line, defining the function is ok
the second line should just replace x with 4 (everywhere that you see x)

so f(x)= 6x+2 evaluated at x=4 is written
f(4) = 6*4 + 2
f(4)= 24+2 = 26

Answer 5

your function is the equation of a line. A line has exactly one y value for every x value
which means it is a function.

Answer 6

ok but now it ask me

Using complete sentences, prove to Splott and Fizzle that your function is a legitimate function

do i prove something

Answer 7

A function is a relation between (x,y) pairs where every x has exactly *one* y value associated with it.

Answer 8

your function is the equation of a line. A line has exactly one y value for every x value
which means it is a function.

Answer 9

You could say, the function f(x)= 6x+2
has the form
y= mx+b
which is the equation of a line. A line has only 1 y value for each x value, so this equation represents a function.

Answer 10

oh ok

Answer 11

for this one
Using your function, explain to the Martians how to solve for f(3). Show your work and explain each step using complete sentences

do u

Answer 12

take my regular function i used and replace 4 with 3 and explain the steps

Answer 13

I would say, replace the x with 3

Answer 14

yea so it would be

f(x)= 6x+2
f(3) = 6*3 + 2
f(3)= 20+2 = 22

Answer 15

I guess your calculator is broken?

Answer 16

how

Answer 17

3*6 is not 20

Answer 18

ohoho i added 2 already and added it again

Answer 19

my bad i forgot it there for the next line

Answer 20

ok, just as long as you figured it out. So the answer is 20

Answer 21

yea sow i just explain the steps

Answer 22

and can i ask u 2 more questions please

Answer 23

?

Answer 24

Using complete sentences, describe to the Martians how to find the inverse of your function.

Answer 25

write the function as
y= 6x+2

now "solve for x"
can you do that ?

Answer 26

do you replace x with y?

Answer 27

You can swap x and y, and then solve for y

or
you solve for x,
then swap x and y

Answer 28

i really dont know how to do this inverse thing can you help

Answer 29

with an examlpe or something

Answer 30

y= 6x+2

now "solve for x"

start by adding -2 to both sides (that means write -2 on both sides of the equation)
can you do that ?

Answer 31

y=x-2

Answer 32

y=1/3(x-2)

Answer 33

y= 6x+2

write -2 on both sides

Answer 34

idk how to do this

Answer 35

y=6x-2

Answer 36

?

Answer 37

almost. but you have an equation. You leave everything as it is
but write -2 on the right side and -2 on the left side

start with
y= 6x+2
now write -2 on both sides:
-2 + y = 6x +2 - 2

Answer 38

the idea is we are "adding -2" or subtracting 2 from each side
now simplify the right side. 2 -2 is ?

Answer 39

0

Answer 40

and 6x+0 is 6x

Answer 41

-2+1 right

Answer 42

y=1

Answer 43

-2 + y = 6x +2 - 2

becomes
-2 + y = 6x +0
and that simplifies to
-2 +y = 6x

order does not matter when adding
so we can also write

y + -2 = 6x

Answer 44

the x's and y's will not disappear. All we are doing is "moving" things around.

so far we have
6x = y-2

now divide both sides by 6

Answer 45

that means draw a line under the left side and write a 6
draw a line under the right side and write a 6

Answer 46

6x/6=y-2/6

Answer 47

yes . but you should write the right side as (y-2)/6
because you are dividing (y-2) by 6 and the way you wrote it looks like y - (2/6)

on the left side you have 6/6 . what is that ?

Answer 48

1

Answer 49

so what do we have so far?

Answer 50

x=(y-2)/6

Answer 51

we have "solved for x"
(x is alone on one side)

last step to find the inverse is swap the x and y

Answer 52

y=(x-2)/6

Answer 53

yes

Answer 54

so that's the answer?

Answer 55

yes, that is the inverse function

Answer 56

ty and my very last question

Answer 57

The Martians ask you to explain one last thing, Ultimate Math Ambassador. They ask you to create a new function, h(x). Then assign any number to x. Using complete sentences, explain whether f(h(x)) and h(f(x)) will always result in the same number. You will use the function f(x) that you created in problem number 2.

Answer 58

you need to make up a new function

Answer 59

f(x)=4x+3

Answer 60

h(x)

Answer 61

Then assign any number to x

I would pick x=0 (keeps the arithmetic easy)

Answer 62

true
h(0)

Answer 63

now figure out
f(h(x)) when x = 0

that means figure out h(0)
and use that number for x in f(x)

Answer 64

h(x)=4x+3
h(0)=4*0+3
h(0)=4+3=7

f(x)= 6x+2
f(0) = 6*0 + 2
f(0)= 6+2 = 8

Answer 65

am i right

Answer 66

you have some of the idea. Let's concentrate on h(0)
once again your calculator is wrong. How did you get from the 2nd the the 3rd line for h(0)
?

Answer 67

i multiply 4*0=4+3=7

Answer 68

4*0 = ?

Answer 69

000

Answer 70

i was rushing

Answer 71

h(x)=4x+3
h(0)=4*0+3
h(0)=0+3=3

Answer 72

so h(0) = 3

now you want to find f( h(0) )
but h(0) is 3, so we want to find f(3)

Answer 73

f(x)= 6x+2
f(3) = 6*3 + 2
f(3)= 18+2 = 20

Answer 74

that means
f(h(0))= 20

now we need to find
h(f(0))

first find f(0)

Answer 75

f(x)= 6x+2 f(0) = 6*0 + 2 f(0)= 6+2 = 8

Answer 76

Gack!

Answer 77

huh

Answer 78

redo what you posted and think about each step.

Answer 79

SAME MISTAKE

Answer 80

f(x)= 6x+2
f(0) = 6*0 + 2
f(0)= 0+2 = 2

Answer 81

ok , f(0)= 2

can you find h(f(0)) ?

Answer 82

no

Answer 83

idk how to do that

Answer 84

remember that f(0) is 2

replace f(0) with 2 in
h(f(0))
what do you get ?

Answer 85

f(x)= 6x+2
f(2) = 6*2 + 2
f(2)= 12+2 = 14

Answer 86

don't take so many steps.

replace f(0) with 2 in
h(f(0))

that means erase f(0) and put in a 2
write down what you get (don't do anything else, no math)

Answer 87

2=6x+2

Answer 88

I want you to get the idea that
h(f(0)) is h(2)

Answer 89

h(2)=6x+2

math is confusing

Answer 90

yes, but if you understand each step, and go slow, you can learn it.
remember, h(x) = 4x+3 , different from f(x)= 6x+2
notice h(2) means replace x with 2 in
h(x)= 4x+3

Answer 91

h(x)=4x+3

Answer 92

h(2)=4x+3

Answer 93

the x should have be replaced with a 2

Answer 94

i did that

Answer 95

all x's
h(2)=4x+3 <--- there is an x that should be a 2

Answer 96

h(2)=4(2)+3

Answer 97

now simplify. 4x with x replaced by 2 is 4*2 4(2) means the same thing, but it's clearer to me to write it as 4*2

h(2)= 4*2 + 3

now simplify

Answer 98

h(2)=8+3=11