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kiruha [24]
3 years ago
7

Does this table represent a function? Why or why not?

Mathematics
2 answers:
Lostsunrise [7]3 years ago
6 0
No because the x value of 8 has two different corresponding y values, 5 and 8, which is not allowed in a function.

Final answer: B
djverab [1.8K]3 years ago
4 0
B. They do not because the x-axis simply can not have the same number
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8 / 3 3/8 as a mixed number in simplest form
sukhopar [10]

Answer:

8/3 as a mixed number would be written as 2 2/3.

8 0
2 years ago
A drawer contains 12 brown socks and 12 black socks, all unmatched. a man takes socks out at random in the dark. the least numbe
Serga [27]
 <span>A) 3 - The third sock will match the first or second if they don't match each other. 
B) 14 - It's highly unlikely yet possible to remove all brown socks first, the next two would have to be black.</span>
6 0
2 years ago
How to solve these 3 problems
Bingel [31]

Answer:

  1. a. decay; b. growth; c. decay; d. neither
  2. r = 4; a = 1; y = 1·4^x
  3. a. an = 3(5^(n-1)); b. f(x) = (3/5)(5^x); c. exponential growth; d. y-intercept: 3/5; first term: 3.

Step-by-step explanation:

There are two kinds of exponential problems here.

  1. exponential functions of the form f(x) = a·b^x
  2. exponential sequences of the explicit form an = a1·r^(n-1)

The second problem gives you a table that suggests the sequence form, but it asks for the exponential function form. The third problem does something similar.

__

<h3>1.</h3>

In an exponential function of the form f(x) = a·b^x, the function grows if b>1 and decays if b<1. Using this check, we can easily answer ...

  a. 0.4 < 1 . . . decay

  b. 1.3 > 1 . . . growth

  c. 1/2 < 1 . . . decay

  d. 1 = 1 . . . neither growth nor decay; the function is constant: j(x) = 1.

__

<h3>2.</h3>

The value of x is given starting at 1, so we can consider this a geometric sequence. The common ratio is r = 16/4 = 4. The first term is a1 = 4, so the explicit formula for the sequence is ...

  an = 4·4^(n-1)

When this is expanded to get rid of the constant in the exponent, we have ...

  an = 4·(4^n)·(4^-1) = 1·4^n

We recognize this form as matching the functional form f(x) = a·r^x. The multiplier of the exponential factor is a=1. In summary, ...

  r = 4; a = 1; f(x) = 1·4^x

__

<h3>3.</h3>

The first term of this geometric sequence is a1 = 3. The common ratio is r = 15/3 = 5. Using the explicit formula, we have ...

 a. explicit form: an = 3·5^(n-1)

Using the method of question 2 to write the functional form, we find ...

  an = 3(5^n)(5^-1) = (3/5)(5^n)

  b. functional form: f(x) = (3/5)(5^x)

  c. function family: exponential growth functions

 d. y-intercept: (3/5) . . . . read this from the f(x) form

     1st term: the first term listed in the given sequence is 3

_____

<em>Additional comment</em>

The "y-intercept" of a sequence is irrelevant (undefined), as the sequence term numbering starts with 1, not 0. The domain of the explicit formula is <em>natural numbers</em>, which does not include 0.

Similarly, the "first term" of a function f(x) needs further definition. Here, we've answered the question by saying the first term is f(1). There is no conventional definition of a "first term" for a continuous function.

3 0
2 years ago
At the beach, the cost for renting a surf board is $39 for 3 hours. At this rate, what will be the charge for renting a surf boa
Blizzard [7]

Answer:

$104 For 8 Hours

Step-by-step explanation:

First figure out the rate for one hour. To figure this out divide $39 by 3. This equals $13. Which means it costs $13 to rent the surfboard for one hour. Finally multiply $13 by 8. This equals $104. Meaning it costs $104 to rent the surfboard for 8 hours.

7 0
2 years ago
What is the slope of the line through (-3, 3) and (-1, -1)?
Vladimir79 [104]

Answer:

The slope is -2

Step-by-step explanation:

To find the slope, we can use the slope formula

m = ( y2-y1)/(x2-x1)

    = (-1 -3)/(-1 - -3)

   = ( -1-3)/(-1+3)

   = -4/2

   = -2

The slope is -2

3 0
2 years ago
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