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4 years ago

What is the logarithmic function modeled by the following table? x f(x) 9 2 27 3 81 4

Mathematics

1 answer:

Aliun [14]4 years ago

7 0

Answer:

The logarithmic function modeled by the given table:

f(x) = log₃x

Step-by-step explanation:

Given Table:

x f(x)

9 2

27 3

81 4

We can see that x increases as powers of 3. And f(x) is the power.

We assume that f(x) = log₃x

Checking using the table:

for x = 9

f(x) = log₃9 = 2

for x = 27

f(x) = log₃27 = 3

for x = 81

f(x) = log₃81 = 4

Hence proved.

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3 years ago

Let g(x, y) = cos(x + 5y). (a) Evaluate g(10, −2). g(10, −2) = (b) Find the domain of g. −1 ≤ x ≤ 1, − 1 5 ≤ y ≤ 1 5 −5 ≤ x ≤ 5,

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4 years ago

Patty and Carl went to the movies. Patty bought the two movie tickets for $7.35 each. Carl bought two buckets of popcorn at $5.6

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3 years ago

What is the slope-intercept form of linear equations?

lara31 [8.8K]

to get the equation of any straight line, we simply need two points off of it, let's use the points from the picture below.

$(\stackrel{x_1}{8}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{12}-\underset{x_1}{8}}}\implies \cfrac{2}{4}\implies \cfrac{1}{2}$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{8}) \\\\\\ y-3=\cfrac{1}{2}x-4\implies y=\cfrac{1}{2}x-1$

if we already have the slope, and we can see the y-intercept on the table, then we can simply use the slopel-intercept form and plug both of them in.

$\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \begin{array}{|c|ll} \cline{1-1} slope\\ \cline{1-1} \cfrac{1}{2}\\ \cline{1-1} y-intercept&\\\cline{1-1} (0~~,~~-1)\\ \cline{1-1} \end{array}~\hfill y=\cfrac{1}{2}x-1$

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2 years ago

The ordered pairs (1, 1), (2, 8), (3, 27), (4, 64), and (5, 125) represent a function. What is a rule that represents this funct

Zarrin [17]

The functions would be:

D. y=x³

We can check it out.

(1,1); x=1; y=1 ⇒1=(1)³=1*1*1=1
(2,8); x=2; y=8 ⇒8=(2)³=2*2*2=8
(3,27); x=3; y=27 ⇒27=3³=3*3*3=27
(4,64): x=4; y=64 ⇒64=4³=4*4*4=64
(5,125); x=5; y=125 ⇔ 125=5³=5*5*5=125

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3 years ago