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Ahat [919]
3 years ago
6

I WILL ARWARD BRAINLIEST!! PLEASE HELP!!

Mathematics
1 answer:
Ivanshal [37]3 years ago
5 0

Answer:

None of the graphs of the equations pass through M(−10, 15).

Step-by-step explanation:

We are given the function y=kx.

It is given that the point B lies on the graph of the given function.

1. B(2, −3)

That is, x= 2 and y= -3

So, y= kx ⇒ -3 = 2k ⇒ k=\frac{-2}{3}

Thus, the function is y=\frac{-2x}{3}

2. B(3\frac{1}{3},-2) i.e. B(\frac{10}{3},-2)

That is, x= \frac{10}{3} and y= -2

So, y= kx ⇒ -2 = \frac{10k}{3} ⇒ k=\frac{-6}{10} ⇒ k=\frac{-3}{5}

Thus, the function is y=\frac{-3x}{5}

From the graph plotted below, we get that,

None of the graphs of the equations pass through M(−10, 15).

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\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}\\\\
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\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}}}
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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}\\\\
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\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
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