Simplify the quotient 3/√7-√3

For the function g(x)=3-8(1/4)^2-x

Reika [66]

Using function concepts, it is found that:

a) The y-intercept is y = 2.5.

b) The horizontal asymptote is x = 3.

c) The function is decreasing.

d) The domain is $(-\infty,\infty)$ and the range is $(-\infty,3)$ .
e) The graph is given at the end of the answer.

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The given function is:

$g(x) = 3 - 8\left(\frac{1}{4}\right)^{2-x}$

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Question a:

The y-intercept is g(0), thus:

$g(0) = 3 - 8\left(\frac{1}{4}\right)^{2-0} = 3 - 8\left(\frac{1}{4}\right)^{2} = 3 - \frac{8}{16} = 3 - 0.5 = 2.5$

The y-intercept is y = 2.5.

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Question b:

The horizontal asymptote is the limit of the function when x goes to infinity, if it exists.

$\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2+\infty} = 3 - 8\left(\frac{1}{4}\right)^{\infty} = 3 - 8\frac{1^{\infty}}{4^{\infty}} = 3 -0 = 3$

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$\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2-\infty} = 3 - 8\left(\frac{1}{4}\right)^{-\infty} = 3 - 8\times 4^{\infty} = 3 - \infty = -\infty$

Thus, the horizontal asymptote is x = 3.

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Question c:

The limit of x going to infinity of the function is negative infinity, which means that the function is decreasing.

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Question d:

Exponential function has no restrictions in the domain, so it is all real values, that is $(-\infty,\infty)$ .
From the limits in item c, the range is: $(-\infty,3)$

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The sketching of the graph is given appended at the end of this answer.

A similar problem is given at brainly.com/question/16533631

8 0

2 years ago

The product of nine and a number is added to six the result is 24 what is the number

Andru [333]

Hello!

We can make an equation based on what we know

The product of 9 and a number is

9 * x

Added to six

9 * x + 6

Gives the result of 24

9 * x + 6 = 24

Now you solve it algebraically

Subtract 6 from both sides

9 * x = 18

Divide both sides by 9

x = 2

The answer is 2

Hope this helps!

8 0

2 years ago

A diameter of a circle has enpoints (-2, 10) and (6, -4) in the standard (x, y) coordinate plane. What is the center of the circ

wlad13 [49]

Answer:

The center of the circle is $C(x,y) = (2, 3)$ .

Step-by-step explanation:

The center of the circle is the midpoint of the segment between the endpoints. We can determine the location of the center by this vectorial expression:

$C(x,y) = \frac{1}{2}\cdot R_{1}(x,y)+ \frac{1}{2}\cdot R_{2}(x,y)$ (1)

Where:

$C(x,y)$ - Center.

$R_{1} (x,y)$ , $R_{2} (x,y)$ - Location of the endpoints.

If we know that $R_{1} (x,y) = (-2,10)$ and $R_{2} (x,y) = (6,-4)$ , then the location of the center of the circle is:

$C(x,y) = \frac{1}{2}\cdot (-2,10)+\frac{1}{2}\cdot (6,-4)$

$C(x,y) = (-1, 5) + (3, -2)$

$C(x,y) = (2, 3)$

The center of the circle is $C(x,y) = (2, 3)$ .

8 0

2 years ago

What is the circumference of a circle with a 12cm diameter?

pochemuha

Answer:

37.7cm

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

a cell phone store sells the basic model of a phone for $30 and the upgraded model for $100 when a customer signs a two-year agr

alisha [4.7K]

30b + 100u = 900
5b + 25u = 200....multiply by -6
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30b + 100u = 900
-30b - 150u = - 1200 (result of multiplying by -6)
------------------add
-50u = - 300
u = 6 <== upgrated phones sold

30b + 100u = 900
30b + 100(6) = 900
30b + 600 = 900
30b = 900 - 600
30b = 300
b = 10 <== basic phones sold

8 0

2 years ago

Read 2 more answers