Answer:
1.20 off dog food
Step-by-step explanation:
<span>D: a and b are odd that should be the answer </span>
Answer:
1. Vertical shrink by a factor of ¹/₅
2. Right 5
3. Up 5
Step-by-step explanation:
Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.
<u>Transformations</u>
For a > 0
![f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}](https://tex.z-dn.net/?f=f%28x%2Ba%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20left%7D)
![f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}](https://tex.z-dn.net/?f=f%28x-a%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20right%7D)
![f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}](https://tex.z-dn.net/?f=f%28x%29%2Ba%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20up%7D)
![f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}](https://tex.z-dn.net/?f=f%28x%29-a%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20down%7D)
![y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a](https://tex.z-dn.net/?f=y%3Da%5C%3Af%28x%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Bstretched%20parallel%20to%20the%20y-axis%20%28vertically%29%20by%20a%20factor%20of%7D%5C%3Aa)
![y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}](https://tex.z-dn.net/?f=y%3Df%28ax%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Bstretched%20parallel%20to%20the%20x-axis%20%28horizontally%29%20by%20a%20factor%20of%7D%20%5C%3A%20%5Cdfrac%7B1%7D%7Ba%7D)
![y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}](https://tex.z-dn.net/?f=y%3D-f%28x%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Breflected%20in%20the%7D%20%5C%3A%20x%20%5Ctextsf%7B-axis%7D)
![y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}](https://tex.z-dn.net/?f=y%3Df%28-x%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Breflected%20in%20the%7D%20%5C%3A%20y%20%5Ctextsf%7B-axis%7D)
Identify the transformations that take the parent function to the given function.
<u>Question 1</u>
![\textsf{Parent function}: \quad f(x)=x^3](https://tex.z-dn.net/?f=%5Ctextsf%7BParent%20function%7D%3A%20%5Cquad%20f%28x%29%3Dx%5E3)
![\textsf{Given function}: \quad f(x)=\dfrac{1}{5}x^3](https://tex.z-dn.net/?f=%5Ctextsf%7BGiven%20function%7D%3A%20%5Cquad%20f%28x%29%3D%5Cdfrac%7B1%7D%7B5%7Dx%5E3)
Comparing the parent function with the given function, we can see that the <u>parent function</u> has been <u>multiplied</u> by ¹/₅.
Therefore, the transformation is:
![y=\dfrac{1}{5}\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:\dfrac{1}{5}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B1%7D%7B5%7D%5C%3Af%28x%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Bstretched%20parallel%20to%20the%20y-axis%20%28vertically%29%20by%20a%20factor%20of%7D%5C%3A%5Cdfrac%7B1%7D%7B5%7D)
As 0 < a < 1, the transformation visually is a compression in the y-direction, so we can also say: Vertical shrink by a factor of ¹/₅
<u>Question 2</u>
![\textsf{Parent function}: \quad f(x)=x^3](https://tex.z-dn.net/?f=%5Ctextsf%7BParent%20function%7D%3A%20%5Cquad%20f%28x%29%3Dx%5E3)
![\textsf{Given function}: \quad f(x)=(x-5)^3](https://tex.z-dn.net/?f=%5Ctextsf%7BGiven%20function%7D%3A%20%5Cquad%20f%28x%29%3D%28x-5%29%5E3)
Comparing the parent function with the given function, we can see that 5 has been <u>subtracted from the x-value</u> of the parent function.
Therefore, the transformation is:
![f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}](https://tex.z-dn.net/?f=f%28x-5%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3A5%5C%3A%5Ctextsf%7Bunits%20right%7D)
<u>Question 3</u>
![\textsf{Parent function}: \quad f(x)=x^3](https://tex.z-dn.net/?f=%5Ctextsf%7BParent%20function%7D%3A%20%5Cquad%20f%28x%29%3Dx%5E3)
![\textsf{Given function}: \quad f(x)=x^3+5](https://tex.z-dn.net/?f=%5Ctextsf%7BGiven%20function%7D%3A%20%5Cquad%20f%28x%29%3Dx%5E3%2B5)
Comparing the parent function with the given function, we can see that 5 has been <u>added to the parent function</u>.
Therefore, the transformation is:
![f(x)+5 \implies f(x) \: \textsf{translated}\:5\:\textsf{units up}](https://tex.z-dn.net/?f=f%28x%29%2B5%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3A5%5C%3A%5Ctextsf%7Bunits%20up%7D)
Learn more about graph transformations here:
brainly.com/question/27845947
Answer:
4.7 * 10^8
Step-by-step explanation:
81 is 45% of 180, all you do is divide 81 by .45 and boom there you go