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3 years ago

The graph shows g(x), which is a translation of f(x)=|x|. Write the function rule for g(x).

Mathematics

1 answer:

Kay [80]3 years ago

8 0

Answer:

g(x) = |x| -9

Step-by-step explanation:

In the form ...

g(x) = a|x -h| +k

the parameters are ...

a: the vertical scale factor (1)
h: the right shift of the vertex (0)
k: the upward shift of the vertex (-9)

The vertex of |x| is (0, 0). The vertex of g(x) is (0, -9), so there has been a vertical shift of -9 and no horizontal shift. The slopes of the lines on the graph of g(x) have a magnitude of 1, so the vertical scale is not changed from the original function (a=1).

Then the translated function is ...

g(x) = |x| -9

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I'll show you how I do it,hope you'll like it.
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2 years ago

Read 2 more answers

Find The art length of a sector with an area of 8 square units.

frez [133]

$\bf \textit{area of a sector of a circle}\\\\
A=\cfrac{\theta \pi r^2}{360}\quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
A=8\\
r=4
\end{cases}\implies 8=\cfrac{\theta \pi 4^2}{360}\implies \cfrac{8\cdot 360}{4^2\pi }=\theta 
\\\\\\
\cfrac{2880}{16\pi }=\theta \implies \boxed{\cfrac{180}{\pi }=\theta }\\\\
-------------------------------\\\\$

$\bf \textit{arc's length}\\\\
s=\cfrac{\theta \pi r}{180}\quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
\theta =\frac{180}{\pi }\\
r=4
\end{cases}\implies s=\cfrac{\frac{180}{\underline{\pi} }\underline{\pi} \cdot 4}{180}\implies s=\cfrac{\underline{180}\cdot 4}{\underline{180}}
\\\\\\
\boxed{s=4}$

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that's pretty much what one-radian stands for, an angle, whose arc is the same length as its radius.

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