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cluponka [151]
2 years ago
7

Which represents a linear function? y=x2 – 3 y= 4x^3 y= 3/4x-2 y=2^x +1

Mathematics
1 answer:
AlexFokin [52]2 years ago
4 0
Y=3/4x-2 is a linear function
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First, we'll want to write out the equation
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then reduce what we can
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so this means n can equal any whole number between 9 4/9 & 12, which gives us the options of {10,11}

n = 10 \: or \: 11
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\bf \qquad \qquad \qquad \qquad \textit{function transformations}&#10;\\ \quad \\\\&#10;&#10;\begin{array}{rllll} &#10;% left side templates&#10;f(x)=&{{  A}}({{  B}}x+{{  C}})+{{  D}}&#10;\\ \quad \\&#10;y=&{{  A}}({{  B}}x+{{  C}})+{{  D}}&#10;\\ \quad \\&#10;f(x)=&{{  A}}\sqrt{{{  B}}x+{{  C}}}+{{  D}}&#10;\\ \quad \\&#10;f(x)=&{{  A}}(\mathbb{R})^{{{  B}}x+{{  C}}}+{{  D}}&#10;\\ \quad \\&#10;f(x)=&{{  A}} sin\left({{ B }}x+{{  C}}  \right)+{{  D}}&#10;\end{array}

\bf \begin{array}{llll}&#10;% right side info&#10;\bullet \textit{ stretches or shrinks horizontally by  } {{  A}}\cdot {{  B}}\\\\&#10;\bullet \textit{ flips it upside-down if }{{  A}}\textit{ is negative}&#10;\\\\&#10;\bullet \textit{ horizontal shift by }\frac{{{  C}}}{{{  B}}}\\&#10;\qquad  if\ \frac{{{  C}}}{{{  B}}}\textit{ is negative, to the right}\\\\&#10;\qquad  if\ \frac{{{  C}}}{{{  B}}}\textit{ is positive, to the left}\\\\&#10;\end{array}

\bf \begin{array}{llll}&#10;&#10;&#10;\bullet \textit{ vertical shift by }{{  D}}\\&#10;\qquad if\ {{  D}}\textit{ is negative, downwards}\\\\&#10;\qquad if\ {{  D}}\textit{ is positive, upwards}\\\\&#10;\bullet \textit{ period of }\frac{2\pi }{{{  B}}}&#10;\end{array}

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

\bf \begin{array}{lllcclll}&#10;y=&2(&1x&-2)^2&-4\\&#10;&\uparrow &\uparrow &\uparrow &\uparrow \\&#10;&A&B&C&D&#10;\end{array}\\\\&#10;-----------------------------\\\\&#10;A\cdot B=2\impliedby \textit{shrunk by a factor of 2, of half-size}\\\\&#10;\cfrac{C}{B}= \cfrac{-2}{1}\implies -2\impliedby \textit{horizontal right shift of 2 units}\\\\&#10;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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