Mathematics, 03.10.2019 09:30 aliviadushane

Given its parent function g(x) = (1/2)^x, what is the equation of the function shown?

Answers: 2

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Answer from: jackienassiri

The correct equation is (B) $f(x)=-2\left(\dfrac{1}{2}\right)^x+1.$

Step-by-step explanation: We are given to select the correct equation of the function f(x) shown in the figure.

From the graph given in the figure, we have

f(-1)=-3,~~f(0)=-1,~~f(1)=0.

(A) First option is

$f(x)=-3\left(\dfrac{1}{2}\right)^x+1.$

From here, we get

$f(-1)=-3\left(\dfrac{1}{2}\right)^{-1}+1=-3\times 2+1=-5\neq -3.$

So, this option is not correct.

(B) First option is

$f(x)=--2\left(\dfrac{1}{2}\right)^x+1.$

From here, we get

$f(-1)=-2\left(\dfrac{1}{2}\right)^{-1}+1=-2\times 2+1=-3\\\\f(0)=-2\left\dfrac{1}{2}\right)^0+1=-2+1=-1,\\\\f(1)=-2\left(\dfrac{1}{2}\right)^1+1=-1+1=0.$

So, this option is correct.

$f(x)=-\left(\dfrac{1}{2}\right)^x-3.$

From here, we get

$f(-1)=-\left(\dfrac{1}{2}\right)^{-1}-3=-1\times 2-3=-5\neq -3.$

So, this option is not correct.

(D) Fourth option is

$f(x)=-\left(\dfrac{1}{2}\right)^x-1.$

From here, we get

$f(-1)=-\left(\dfrac{1}{2}\right)^{-1}-1=--\times 2-1=-3,\\\\f(0)=-\left\dfrac{1}{2}\right)^0-1=-1-1=-2\neq -1.$

So, this option is not correct.

Thus, the correct function is

(B) $f(x)=-2\left(\dfrac{1}{2}\right)^x+1.$

Answer from: dannisundrop

$\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}}
\end{array}$

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

so... notice, the graph is just g(x), flipped upside-down and shifted up by 1 unit

Answer from: Quest

The answers are 20,30,80,180,960,890,1230,4560. on the first row
Can someone me with this! it’s for my little sister and she’s not sure what she has to do. asap

Can someone me with this! it’s for my little sister and she’s not sure what she has to do. asap

Answer from: Quest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

75% of the temperatures are below what value? how do you know? 75% of the temperatures are above w

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