Answer:
The cyclists should be riding 20 miles every day. (Which is a lot for me)
Step-by-step explanation:
All we have to do to find how many Miles per Day, is to divided the miles by the days.
120 ÷ 6 = 20
So, the cyclists should be riding 20 miles every day.
The answers are A, C, A in the order they are listed
Answer:
<u>Translations</u>
For ![a > 0](https://tex.z-dn.net/?f=a%20%3E%200)
![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)
<h3><u>
Question 1</u></h3>
Given: ![f(x)=(2,-3)](https://tex.z-dn.net/?f=f%28x%29%3D%282%2C-3%29)
![f(x)+2 \implies (x, y+2)= (2,-3+2)=(2,-1)](https://tex.z-dn.net/?f=f%28x%29%2B2%20%5Cimplies%20%28x%2C%20y%2B2%29%3D%20%282%2C-3%2B2%29%3D%282%2C-1%29)
![f(x)-3 \implies (x,y-3)=(2,-3-3)=(2,-6)](https://tex.z-dn.net/?f=f%28x%29-3%20%5Cimplies%20%28x%2Cy-3%29%3D%282%2C-3-3%29%3D%282%2C-6%29)
![f(x+5)\implies (x-5,y)=(2-5,-3)=(-3,-3)](https://tex.z-dn.net/?f=f%28x%2B5%29%5Cimplies%20%28x-5%2Cy%29%3D%282-5%2C-3%29%3D%28-3%2C-3%29)
![-f(x) \implies (x,-y)=(2,-(-3))=(2,3)](https://tex.z-dn.net/?f=-f%28x%29%20%5Cimplies%20%28x%2C-y%29%3D%282%2C-%28-3%29%29%3D%282%2C3%29)
![f(-x) \implies (-x,y)=(-(2),-3)=(-2,-3)](https://tex.z-dn.net/?f=f%28-x%29%20%5Cimplies%20%28-x%2Cy%29%3D%28-%282%29%2C-3%29%3D%28-2%2C-3%29)
![f(2x) \implies \left(\dfrac{x}{2},y\right)=\left(\dfrac{2}{2},-3\right)=(1,-3)](https://tex.z-dn.net/?f=f%282x%29%20%5Cimplies%20%5Cleft%28%5Cdfrac%7Bx%7D%7B2%7D%2Cy%5Cright%29%3D%5Cleft%28%5Cdfrac%7B2%7D%7B2%7D%2C-3%5Cright%29%3D%281%2C-3%29)
![2f(x) \implies (x,2y)=(2,2 \cdot -3)=(2,-6)](https://tex.z-dn.net/?f=2f%28x%29%20%5Cimplies%20%28x%2C2y%29%3D%282%2C2%20%5Ccdot%20-3%29%3D%282%2C-6%29)
![-f(x-4) \implies (x+4,-y)=(2+4,-(-3))=(6,3)](https://tex.z-dn.net/?f=-f%28x-4%29%20%5Cimplies%20%28x%2B4%2C-y%29%3D%282%2B4%2C-%28-3%29%29%3D%286%2C3%29)
![\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} & & & & & & &\\f(x)+2 & f(x)-3 & f(x+5) & -f(x) & f(-x) & f(2x) & 2f(x) & -f(x-4)\\& & & & & & &\\\cline{1-8} & & & & & & &\\(2,-1) & (2,-6) & (-3,-3) & (2,3) & (-2,-3) & (1,-3) & (2,-6) & (6,3)\\& & & & & & &\\\cline{1-8} \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7B%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%7D%5Ccline%7B1-8%7D%20%26%20%26%20%26%20%26%20%26%20%26%20%26%5C%5Cf%28x%29%2B2%20%26%20f%28x%29-3%20%26%20f%28x%2B5%29%20%26%20-f%28x%29%20%26%20f%28-x%29%20%26%20f%282x%29%20%26%202f%28x%29%20%26%20-f%28x-4%29%5C%5C%26%20%26%20%26%20%26%20%26%20%26%20%26%5C%5C%5Ccline%7B1-8%7D%20%26%20%26%20%26%20%26%20%26%20%26%20%26%5C%5C%282%2C-1%29%20%26%20%282%2C-6%29%20%26%20%28-3%2C-3%29%20%26%20%282%2C3%29%20%26%20%28-2%2C-3%29%20%26%20%281%2C-3%29%20%26%20%282%2C-6%29%20%26%20%286%2C3%29%5C%5C%26%20%26%20%26%20%26%20%26%20%26%20%26%5C%5C%5Ccline%7B1-8%7D%20%5Cend%7Barray%7D)
<h3><u>Question 2</u></h3>
Parent function: ![y=x^2](https://tex.z-dn.net/?f=y%3Dx%5E2)
Given function: ![f(x)=(x+8)^2-4](https://tex.z-dn.net/?f=f%28x%29%3D%28x%2B8%29%5E2-4)
![f(x+8) \implies f(x) \: \textsf{translated}\:8\:\textsf{units left}](https://tex.z-dn.net/?f=f%28x%2B8%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3A8%5C%3A%5Ctextsf%7Bunits%20left%7D)
![f(x)-4 \implies f(x) \: \textsf{translated}\:4\:\textsf{units down}](https://tex.z-dn.net/?f=f%28x%29-4%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3A4%5C%3A%5Ctextsf%7Bunits%20down%7D)
Therefore, <u>a translation 8 units to the left and 4 units down.</u>
0.36 as a fraction would be 9/25