Plz answer ASAP!

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

What is the reason for each step in the solution of the equation? 18−2x=4x

Reika [66]

In order to solve an equation for a certain variable, you should isolate that variable on one side of the equation and leave all the other terms on the other side on the equation.
The, you solve to get the value of the variable.

The equation we have here is:
<span>18−2x=4x
First, we need to isolate the terms containing the "x" on one side of the equation. To do this, we will add 2x to both sides of the equation:
</span><span>18−2x+2x=4x+2x
18 = 6x
Now, we need to get the value of the "x". To do this, we will simply divide both sides of the equation by 6:
18/6 = 6x/6
3 = x .............> This is the solution of the equation</span>

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2 years ago

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riadik2000 [5.3K]

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Find the total amount in the compound interest account.

ivanzaharov [21]

11340

9% of 7000 is 630 then just multiply 630x18 which equals to 11340