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3 years ago

Which graph best represents f(x)=|x|

Mathematics

1 answer:

jasenka [17]3 years ago

5 0

The graph of f(x) = |x| would look like the image below.

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Write a formula for function f in terms of function g.

emmasim [6.3K]

$\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}$

so hmm if you notice, your f(x) there, looks just like g(x), but is "shifted horizontally" by about 9 units to the right

that simply means, based on that template above, that C/B = -9, and we can simply make B = 1 and C = -9, and we get C/B = -9/1 which is -9

thus $\bf \begin{array}{llcll}
f(x)=g(&1x&-9)\\
&\uparrow &\uparrow \\
&B&C
\end{array}\iff f(x)=g(x-9)$

7 0

3 years ago

Jaxon and Isaac live different directions from the city center. Jaxon lives 10 blocks east and 5 blocks north. Isaac lives 8 blo

givi [52]

Answer:

Step-by-step explanation:

As shown in the figure attached Jaxon is 10 blocks east and 5 blocks north.

So x-coordinates of Jaxon will be 10 units and y-coordinates will be 5 units.

and coordinates will be (10,5)

Similarly coordinates of Isaac will be defined by his distance towards west and distance towards south.

So x-coordinates will be 8 units and y-coordinates will be 15 units.

Therefore, coordinates of Isaac will be (-8,-15).

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3 years ago

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How to solve a log equation with variable in the exponent?

GREYUIT [131]

Example...

4^x = 16
log(4^x) = log(16)
x*log(4) = log(16)
x = log(16) / log(4)

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4 years ago

Alex purchased 29 4x6 prints and 16 5x7 prints from an online printing service and paid $22.89. If 5x7 prints cost $0.84 more th

viktelen [127]

Answer:

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3 years ago

Explain why the APR does not compare loans for different lengths of time

Usimov [2.4K]

Answer:

APR does not tell you how long your rate is locked for. A 15-year loan may have a lower interest rate, but could have a higher APR, since the loan fees are amortized over a shorter period of time. It is not wise to compare a 30-year loan with a 15-year loan using their respective APRs.

Step-by-step explanation:

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