Question

The pool company developed new chemicals that transform the pH scale. Using the pH function p(t) = −log10t as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Use complete sentences and show all translations on your graph.
p(t) + 1
p(t + 1)
−1 • p(t)

Answer 1

@ganeshie8 @mathmale @whpalmer4 @mathstudent55

Answer 2

If you ever swam in a pool and your eyes began to sting and turn red, you felt the effects of an incorrect pH level. pH measures the concentration of hydronium ions and can be modeled by the function p(t) = −log10t. The variable t represents the amount of hydronium ions; p(t) gives the resulting pH level.

Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3.

Answer 3

I've tried graphing on GeoGebra, but it wont graph unless I create sliders

Answer 4

p(t)= -log10t

so than you know this function how you will get y ?

Answer 5

switch p(t) to y

Answer 6

yes right so than you know that

y = -log10t

what is the base of log in this case ?

Answer 7

10

Answer 8

\[y=\log_{10}(t) \]

Answer 9

so than

y = - lg(t) yes ?

Answer 10

what happened to the 10 and the o

Answer 11

so try calculi p(t) +1 = ?
p(t+1) = ? and
-1*p(t) = ?

what will get ?

Answer 12

i dont understand what goes in place of question mark

Answer 13

why ? these all are inside the text of this exercise - yes ? so you have wrote there above

Answer 14

This is my weakest topic of algebra 2, and i dont get it that well.

Answer 15

so for example when you need graph a function f(x)= x +2

how you get and how you know what will be the x an y value what you need marking on the graph using axes x and y ?

so just use these knowledge in this case of exercise too

Answer 16

p(t) will be y and t sign x - yes ?

Answer 17

sure

Answer 18

so than just use them here now

Answer 19

so y+1=?

Answer 20

y=?

Answer 21

i still dont get it

Answer 22

just assum to y the 1

Answer 23

p(t) = - lg t yes ? so
p(t)+1 = -lg t +1
but you can rewriting 1 = lg 10 so than p(t)+1 = -lg t + lg 10

can you continue it ?

Answer 24

no, you are explaining it well, i just dont get it at all

Answer 25

so you know that lg a + lg b = lg (a*b)

yes ?

Answer 26

yes

Answer 27

- lg t = lg t^(-1) = lg 1/t --- so is this true ?

Answer 28

ye

Answer 29

p(t)+1 = -lg t + lg 10 = lg 1/t + lg 10 = lg 10/t - right ?

Answer 30

i guess

Answer 31

so now try calculi it the second case - ok ?

Answer 32

p(t+1)=?

Answer 33

yes

Answer 34

p(t+1)=-log(t+1)

Answer 35

so and with minus in front of log what you make ?

Answer 36

log(t+1)^-1

Answer 37

p(t)+1 = lg 10/t

try get it in this style

Answer 38

so than p(t+1) = ?

Answer 39

ill try

Answer 40

log10*t

Answer 41

how you have got it so ?

Answer 42

@dukelaxfan: Is this the problem in which you want help? If no, please say specifically what you need to know / learn.

Answer 43

learn how to get the answers

Answer 44

i dont get what jhonyy it trying to teach me

Answer 45

ok. @mathmale please try it you

Answer 46

@DukeLaxFan you dont wan to graph these points for you can get the tranformations of y ?

Answer 47

Duke, again I ask YOU to explain in words what you want to know.

Answer 48

Yes, I need to graph them

Answer 49

@DukeLaxFan you have wrote this above - yes ?
explain which transformation results in a y-intercept and why. You may graph by hand

Answer 50

or technology

Answer 51

i want to know how Using the pH function p(t) = −log10t as the parent function, explain which transformation results in a y-intercept and why

Answer 52

and i can graph using technology if its relevant

Answer 53

OK. Graph the parent function, p(t) = −log10t.
Use the Draw utility, below.

Answer 54

can i just put a picture of it

Answer 55

You could use your graphing calculator for this and then copy the graph to the Draw utility, or take and upload a photo of your calculator screen.

Answer 56

Very nice graph, appropriate.
Now, suppose you take the parent function p(t) and re-write it by adding 6. What happens to the graph? Use the online graphing utility if possible to show this.

Answer 57

sarcasm?.

Answer 58

Absolutely not! What makes you think I'm being sarcastic?

Answer 59

just making sure

Answer 60

Let's concentrate on the math problem at hand.

Answer 61

yessir

Answer 62

so p(t)+6=-log(10)(t)

Answer 63

Actually, it'd be -log t + 6.
Use a different name: p2 (t) = -log t + 6 since you are changing the original function, p(t).

Answer 64

do i include the base aswell?

Answer 65

No. p(t) = −log10t. p2(t)=-log t + 6. Graph this new function.

Note: I am not ignoring your (10) when you write log(10)t. "log t" implies base 10, so it's not necessary to write (10).

Answer 66

oh ok, i didnt know

Answer 67

So, graph this new function p2(t) as you did p(t), EXCEPT now add 6 to the function (right side ONLY).

Let's see your graph.

Answer 68

i couldnt do the p2 for some reason

Answer 69

My wifi is acting up

Answer 70

hope that works

Answer 71

Your graph of p2(t) is fine. Does it have a y-intercept?

Answer 72

i dont think so, if it does, ittle take me an hour to find

Answer 73

the whole point is to determine whether or not each version of the original graph has a y-intercept. p(t) and p2(t) do NOT. right?

Answer 74

no

Answer 75

Right. Now type out p(t) again.
Next, throw out the 't' and replace it with (t+1).

Answer 76

it says i need sliders

Answer 77

???

p(t) = -log t
Throw out the t: p( ) = - log ( )
Write "t+1" where the "t" was.

Answer 78

sorry zeronknight

Answer 79

test

Answer 80

Good morning!

Next move: graph p(t+1). Do you recognize this as a form of

p(t-a) or p(t+b)?
In the case of p(t-a), move your entire graph "a" units to the RIGHT.
In the case of p(t+b), move your entire graph "b" units to the LEFT.

This is called "horizontal translation."

Answer 81

Same to you. Yes I remember the horizontal and vertical shifts

Answer 82

So, you have this lovely graph of p(t)=-log t.
Will you be translating this graph to left or to the right as you portray p(t+1)?

Answer 83

left

Answer 84

Right. We translate the graph to the left. Graph this new function p(t+1). Does the graph intersect the y-axis? If so, at what point (approx.)?

Answer 85

p(t+1)=-log(t)?

Answer 86

anytime i try to graph it, it says to create sliders

Answer 87

Im gonna be afk for a few