Samantha created part of a table to show her savings. She saved at the same rate each week. Which graph shows this relationship?
2 answers:
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Answer:
For a rectangular prism-like swimming pool: .
when
,
and
.
Step-by-step explanation:
Let assume that swimming pool has a rectangular base and depth is the same at any point at the bottom. In addition, let and
be the width and length of the swimming pool. Then, the volume needed to fill the swimming pool is:
, where
is the depth of the pool.
Let be ,
and
. The volume of the swimming pool is:
2. means that for every x, there is eactly one y
basically, we can use the vertical line test to see if it crosses at any 2 points
first one works
2nd one works
3rd works
4th works
5th works
they are all one to one functions
3.
easy
steps
for f(x)=?
replace f(x) with y
switch x and y
solve for y
replace y with f⁻¹(x)
so
replace
switch
solve
![\sqrt[3]{x+2}=1+y](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%2B2%7D%3D1%2By)
![-1+\sqrt[3]{x+2}=](https://tex.z-dn.net/?f=-1%2B%5Csqrt%5B3%5D%7Bx%2B2%7D%3D)
replace
![f^{-1}(x)=-1+\sqrt[3]{x+2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D-1%2B%5Csqrt%5B3%5D%7Bx%2B2%7D)
first option
4.
domain, hmm we can't divide by 0 so domain is all real numbers except for x=0
domain is
hmm, range
as x approaches negative or positive infinity, f(x)=5
as x approaches 0 from the left, f(x) appraoches negative infintiy
as x approaches 0 from the right , f(x) appraoches positive infintiy
so range is
domain is
range is
answer is the 4th option
basically, we can use the vertical line test to see if it crosses at any 2 points
first one works
2nd one works
3rd works
4th works
5th works
they are all one to one functions
3.
easy
steps
for f(x)=?
replace f(x) with y
switch x and y
solve for y
replace y with f⁻¹(x)
so
replace
switch
solve
replace
first option
4.
domain, hmm we can't divide by 0 so domain is all real numbers except for x=0
domain is
hmm, range
as x approaches negative or positive infinity, f(x)=5
as x approaches 0 from the left, f(x) appraoches negative infintiy
as x approaches 0 from the right , f(x) appraoches positive infintiy
so range is
domain is
range is
answer is the 4th option