Please help with my math

Troyanec [42]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\

\begin{array}{rllll} 
% left side templates
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}$

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\end{array}$

$\bf \begin{array}{llll}


\bullet \textit{ vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}
\end{array}$

now, with that template in mind, let's take a peek at this function

$\bf \begin{array}{lllcclll}
y=&2(&1x&-2)^2&-4\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}\\\\
-----------------------------\\\\
A\cdot B=2\impliedby \textit{shrunk by a factor of 2, of half-size}\\\\
\cfrac{C}{B}= \cfrac{-2}{1}\implies -2\impliedby \textit{horizontal right shift of 2 units}\\\\
D=-4\impliedby \textit{vertical down shift of 4 units}$

so, the graph of y=2(x-2)²-4, is really the same graph of y=x², BUT, narrower, and moved about horizontally and vertically

8 0

3 years ago

Read 2 more answers

Expand <br><br> 2y (2y + 8 )

Andrews [41]

Hello There!

2y x 2y = 4y²
2y x 8 = 16y.
Put it together and you get the answer of:
4y² + 16y.

Hope This Helps You!
Good Luck :)

- Hannah ❤

7 0

3 years ago

If T(n) = 3n -5 what is the 3rd term

PtichkaEL [24]

Tn=3n-5 therefore: T(3)=3(3)-5 T(3) =4

4 0

3 years ago

An empty 5-gal water jug weighs 0.75 lb. With 3 c of water inside, the jug weighs 2.25 lb. Which equation models the jug's weigh

Deffense [45]

Weight of 1 c
3 c = 2.25 - empty bucket
3 c = 2.25 - 0.75
3 c = 1.5
c = 1.5/3 =1/2

Jug Weigh = (1/2)x +0.75

8 0

3 years ago

Mrs. Fronkos class for evry 6 boys there are 8 girls. Write the ratio of boys to girls in simplest form

Rama09 [41]

Answer:

3:4

Step-by-step explanation:

there are 6 boys for every 8 girls, so the initial ratio is 6:8. however, this can be simplified by finding a number both 6 and 8 are evenly divisible by. In this case, you can divide the ratio by 2. 6/2 = 3 and 8/2 = 4, which is why the simplified form is 3:4

5 0

3 years ago

Please help with my math ​

Please help with my math