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3 years ago

Function A and Function B are linear functions

Mathematics

1 answer:

melomori [17]3 years ago

5 0

Answer:

Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. ... b is the coefficient of the independent variable

Step-by-step explanation:

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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.

------------------------------------

The given function is:

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

------------------------------------

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.

------------------------------------

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.

--------------------------------------------------

Question c:

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

--------------------------------------------------

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: $(-\infty,3)$

--------------------------------------------------

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

3 years ago

The graph below represents the number of pieces of paper that are found in boxes. What is the constant of proportionality?

kotegsom [21]

Answer:

12.5

Step-by-step explanation:

It is equal to the slope of the line = 50/4 = 12.5

5 0

2 years ago

(6t - 4.5) * (4.5t + 8) Can someone help?

nasty-shy [4]

Answer:

Step-by-step explanation: Ok so the t(s) = 1 Ok?.... 4.5+8 = 12.5 you will need to keep that in mind ok?.... 6 - 4.5 = 1.5.

...So 12.5 x 1.5 = 18.75

Here is your Answer: 18.75

6 0

3 years ago

Julio bought soccer shoes at a $35% off sale and saved $42. What was the regular price of the shoes?

Alborosie

Answer:

$120

Step-by-step explanation:

35% : 42

100% : X

42/35 = X/100

X = 100×42/35

X = $120

8 0

3 years ago

Read 2 more answers

-4r + 1 = -2r - 17 a. 9 b. 11 c. -18 d. -16

alukav5142 [94]

The answer would be 9

6 0

3 years ago