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gavmur [86]
3 years ago
5

The graph of the function f(x) = –(x + 1)2 is shown. Use the drop-down menus to describe the key aspects of the function.

Mathematics
2 answers:
inna [77]3 years ago
6 0

A function f from a set A to a set B is a relation that assigns to each element x in the set A exactly one element y in the set B. The set A is the domain (also called the set of inputs) of the function and the set B contains the range (also called the set of outputs).


The graph of a function f is the collection of ordered pairs (x,f(x)) such that x is in the domain of f being:

x the directed distance from the y-axis.

y=f(x) the directed distance from the x-axis.


By plotting the function f(x)=-(x+1)^2 we get the graph illustrated below.  



From this graph, we know that:

  • The vertex is the maximum value
  • The function is positive for no values of x
  • The function is decreasing when x>-1
  • The domain of the function is all real numbers
  • The range of the function is all real numbers less or equal to 0

Sav [38]3 years ago
3 0

Solution:

The function is, f(x)= -(x+1)^2

It can be Written as, (x+1)^2=-y

The given equation is of Parabola, opening below , X axis.

The vertex of Parabola is , (-1 , 0).

Comparing with general equation of Parabola ,

x^2=4 a y\\\\ 4 a = -1\\\\ a=\frac{-1}{4}

The focus of the given parabola is obtained by, putting , x+1=0,gives, x=-1,So focus will be, (-1,\frac{-1}{4})

And equation of Directrix is, y=\frac{1}{4}

Line, x=-1, divides the parabola into two symmetrical Parts.

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What is an explicit formula for the geometric sequence -64,16,-4,1,... where the first term should be f(1).
nirvana33 [79]

Answer:

a_{n} = -64(-\frac{1}{4})^{n-1}

it seems like the first term is -64, so lets write the formula accordingly:

a_n = a1(r)^(n-1)

where 'n' is the number of terms

a1 is the first term of the sequence

'r' is the ratio

the ratio is -\frac{1}{4} because -64 * -\frac{1}{4} = 16 and so on...

the explicit formula is :

a_{n} = -64(-\frac{1}{4} )^{n-1}

7 0
3 years ago
A population of bacteria begins with 1500 bacteria and grows to 4500 in one hour.
dezoksy [38]

The function that represents the growth of this culture of bacteria as a function of time is; P = 1500e^(1.0986t)

<h3>How to calculate Exponential Growth?</h3>

The formula for exponential growth is;

P = P₀e^(rt)

where;

P = current population at time t

P₀ = starting population

r = rate of exponential growth/decay

t = time after start

Thus, from our question we have;

4500 = 1500 * e^(r * 1)

4500/1500 = e^r

e^r = 3

In 3 = r

r = 1.0986

Thus, the function that represents the growth of this culture of bacteria as a function of time is;

P = 1500e^(1.0986t)

For the culture to double, then;

P/P₀ = 2. Thus;

e^(1.0986t) = 2

In 2 = 1.0986t

t = 0.6931/1.0986

t = 0.631 hours

Read more about Exponential Growth at; brainly.com/question/27161222

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A,D can I get my Brainly
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Find the perimeter of this triangle.<br> 10 cm<br> 17 cm<br> 8 cm<br> 21 cm<br> P = [ ?] cm
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Answer:

perimeter=21+17+10

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If joe has 30$ in his bank account how much will he have if he deposits 1/3 of his paycheck each month for 6 months? His home pa
kakasveta [241]

Answer:

$870 in his bank account

Step-by-step explanation:

420 / 3 = 140

140 * 6 = 840

840 + 30 = 870

4 0
3 years ago
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