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)
@imqwerty

Answer 1

um wym by this drawing tho^ :)

Answer 2

omg
the 10 lol is smaller

Answer 3

p(t) = −log10t

Answer 4

yes you write liek this^ i will understand :)
so the options are these r8?-
p(t) + 1=\( -log_{10}t\)
p(t + 1)=\( -log_{10}t\)
−1 • p(t)=\( -log_{10}t\)

Answer 5

yes :)

Answer 6

Ok I have to show all the translations on the graph though but i dont know how to use this website lol

Answer 7

alright i made a mistake reading the question >:(

heres the correct answer tho-

\(p(t)\) means the y coordinate
and
\(t\) means the x coordinate

so for graph to intersect the y axis the x coordinate must be 0

so

check the 1st option
\(p(t)+1=-log(t)\)

here (t) cannot be 0 because logarithm of 0 is not defined
so this is not the answer

now check the 2nd option

it says-
\(p(t+1)=-log(t+1)\)

here \(t\) can be 0 :) because unlike in previous option where we were getting \(log(0)\) on keeping t=0 here we don't get that because of that "1" with the t

so this option is correct

Answer 8

the translation is->
shift the function left by -1

Answer 9

When it says "show all translations on your graph" that means to put
p(t)+1
p(t+1)
-1*p(t)
on the graph with the orginal one right?

Answer 10

ohh yes yes

Answer 11

p(t) + 1->shifting the graph up by 1
p(t + 1)->shifting the graph left by -1
−1 • p(t) -> flipping the graph upside down

the translations do this^
and we already discussed which one will make the graph intersect y axis

Answer 12

Alrighty \(\large\color{green}{Thank~you!!!!}\)

Answer 13

np :)