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DanielleElmas [232]
2 years ago
6

What are the amplitude, period, phase shift, and midline of f(x) = 2 sin(x + π) − 4?

Mathematics
1 answer:
MrRissso [65]2 years ago
6 0

\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ % templates f(x)=Asin(Bx+C)+D \\\\ f(x)=Acos(Bx+C)+D\\\\ f(x)=Atan(Bx+C)+D \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \bullet \textit{ stretches or shrinks}\\ ~~~~~~\textit{horizontally by amplitude } A\cdot B\\\\ \bullet \textit{ flips it upside-down if }A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis}


\bf \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{function period or frequency}\\ ~~~~~~\frac{2\pi }{B}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ ~~~~~~\frac{\pi }{B}\ for\ tan(\theta),\ cot(\theta)


with that template in mind, let's take a peek


\bf f(x)=2sin(x+\pi )-4\implies f(x)=\stackrel{A}{2}sin(\stackrel{B}{1}x\stackrel{C}{+\pi })\stackrel{D}{-4} \\\\[-0.35em] ~\dotfill\\\\ \textit{Amplitude}\implies 2 \\\\\\ \stackrel{phase}{\textit{Horizontal Shift}}\implies \cfrac{C}{B}\implies \cfrac{+\pi }{1}\implies +\pi \impliedby \pi \textit{ units to the left} \\\\\\ \textit{Period}\implies \cfrac{2\pi }{B}\implies \cfrac{2\pi }{1}\implies 2\pi \\\\\\ \textit{Vertical Shift}\implies D\implies -4\impliedby \textit{4 units downwards}


now, the midline for the parent function of sin(x) is simply the x-axis, namely y = 0.

this shifted/transformed version of it, has a vertical shift of 4 units down, so the midline moved from y = 0, to y = -4.

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At a temperature of t degrees​ Fahrenheit, sound travels s feet per​ second, where s equals 21.9 StartRoot 5 t plus 2457 EndRoot
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Answer:

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Step-by-step explanation:

The function:

s = 21.9 \; \sqrt{ 5 t + 2457 }

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We know that sound traveled at a rate of 1121 ​ft/sec. To find the temperature we need to replace with s value and isolate t for the above function.

1121 = 21.9 \; \sqrt{ 5 t + 2457 }

\frac{1121}{21.9} = \sqrt{ 5 t + 2457 }

51.19^2 = 5 t + 2457

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\frac{163.13}{5} = t

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Answer:

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Step-by-step explanation:

3.2     Factoring  2x2 + 7x + 3

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The middle term is,  +7x  its coefficient is  7 .

The last term, "the constant", is  +3

Step-1 : Multiply the coefficient of the first term by the constant   2 • 3 = 6

Step-2 : Find two factors of  6  whose sum equals the coefficient of the middle term, which is   7 .

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     1    +    6    =    7    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  6

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Step-4 : Add up the first 2 terms, pulling out like factors :

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Step-5 : Add up the four terms of step 4 :

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            Which is the desired factorization

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A basketball team has 2 point guards, 3 shooting guards, 3 small forwards, 3 power forwards, and 2 centers. How many line-ups ar
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Answer:

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Answer:

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