![\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis}](https://tex.z-dn.net/?f=%5Cbf%20~%5Chspace%7B10em%7D%5Ctextit%7Bfunction%20transformations%7D%20%5C%5C%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllll%7D%20f%28x%29%3D%20A%28%20Bx%2B%20C%29%5E2%2B%20D%20%5C%5C%5C%5C%20f%28x%29%3D%20A%5Csqrt%7B%20Bx%2B%20C%7D%2B%20D%20%5C%5C%5C%5C%20f%28x%29%3D%20A%28%5Cmathbb%7BR%7D%29%5E%7B%20Bx%2B%20C%7D%2B%20D%20%5Cend%7Barray%7D%5Cqquad%20%5Cqquad%20%5Cbegin%7Barray%7D%7Bllll%7D%20f%28x%29%3D%5Ccfrac%7B1%7D%7BA%28Bx%2BC%29%7D%2BD%20%5C%5C%5C%5C%5C%5C%20f%28x%29%3D%20A%20sin%5Cleft%28%20B%20x%2B%20C%20%5Cright%29%2B%20D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20stretches%20or%20shrinks%20horizontally%20by%20%7D%20A%5Ccdot%20B%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20flips%20it%20upside-down%20if%20%7D%20A%5Ctextit%7B%20is%20negative%7D%5C%5C%20~~~~~~%5Ctextit%7Breflection%20over%20the%20x-axis%7D)
![\bf \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbullet%20%5Ctextit%7B%20flips%20it%20sideways%20if%20%7D%20B%5Ctextit%7B%20is%20negative%7D%5C%5C%20~~~~~~%5Ctextit%7Breflection%20over%20the%20y-axis%7D%20%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20horizontal%20shift%20by%20%7D%5Cfrac%7B%20C%7D%7B%20B%7D%5C%5C%20~~~~~~if%5C%20%5Cfrac%7B%20C%7D%7B%20B%7D%5Ctextit%7B%20is%20negative%2C%20to%20the%20right%7D%5C%5C%5C%5C%20~~~~~~if%5C%20%5Cfrac%7B%20C%7D%7B%20B%7D%5Ctextit%7B%20is%20positive%2C%20to%20the%20left%7D%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20vertical%20shift%20by%20%7D%20D%5C%5C%20~~~~~~if%5C%20D%5Ctextit%7B%20is%20negative%2C%20downwards%7D%5C%5C%5C%5C%20~~~~~~if%5C%20D%5Ctextit%7B%20is%20positive%2C%20upwards%7D%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20period%20of%20%7D%5Cfrac%7B2%5Cpi%20%7D%7B%20B%7D)
with that template in mind.
![\bf \stackrel{parent}{y = \cfrac{1}{x}}\qquad \qquad y=\cfrac{1}{x+\underset{\underset{-5}{\uparrow }}{C}}+\stackrel{\stackrel{-10}{\downarrow }}{D}\implies \cfrac{1}{x-5}-10](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bparent%7D%7By%20%3D%20%5Ccfrac%7B1%7D%7Bx%7D%7D%5Cqquad%20%5Cqquad%20y%3D%5Ccfrac%7B1%7D%7Bx%2B%5Cunderset%7B%5Cunderset%7B-5%7D%7B%5Cuparrow%20%7D%7D%7BC%7D%7D%2B%5Cstackrel%7B%5Cstackrel%7B-10%7D%7B%5Cdownarrow%20%7D%7D%7BD%7D%5Cimplies%20%5Ccfrac%7B1%7D%7Bx-5%7D-10)
C = -5................. horizontal shift to the right of 5 units.
D = - 10.............. vertical shift downwards of 10 units.
Answer:
the thrid one
Step-by-step explanation:
The answer is 18 inches.
432 / 24 = 18
area / length = width
Answer:
cCompute the value of x if angle a=35 ° angle b=45° angle c=50°. 2. See answers. Log in to add comment. Answer. 2.3/5. 2. 123jiya73. Helping ...
Answer:
The correct option is 1
Step-by-step explanation:
Given the number . we have to identify the number is rational or irrational
As we know is irrational
i.e
The above number is irrational as it is non repeating and non-termination number after decimal.
As the sum of a rational and an irrational must be irrational
∴ is irrational which gives the sum 3.31227766....
hence, the correct option is 1)