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Inessa05 [86]
2 years ago
11

Please help with this question

Mathematics
1 answer:
ratelena [41]2 years ago
8 0

Answer: (2) =

(−3) =

(−1) =

(−4) =

(0) =

(−4) =

(−1) =

(3)  =

() = �

−2 + 1, < 0

2

3

− 3, ≥ 0 () = �

5, ≤ 2

2 − 4, >

Step-by-step explanation: Piecewise Function

(a solid dot means "including",

an open dot means "not including")

And this is how we write it:

Piecewise Function

The Domain (all the values that can go into the function) is all Real Numbers up to and including 6, which we can write like this:

Dom(f) = (-∞, 6] (using Interval Notation)

Dom(f) = {x member of Reals | x ≤ 6} (using Set Builder Notation)

And here are some example values:

X Y

−4 16

−2 4

0 0

1 1

2 6

3 7

Example: Here is another piecewise function:

continuous jump fn h(x) = 2 if x<=1, x if x>1

which looks like:   continuous jump graph h(x)

What is h(−1)?

x is ≤ 1, so we use h(x) = 2, so h(−1) = 2

What is h(1)?

x is ≤ 1, so we use h(x) = 2, so h(1) = 2

What is h(4)?

x is > 1, so we use h(x) = x, so h(4) = 4

Piecewise functions let us make functions that do anything we want!

Example: A Doctor's fee is based on the length of time.

Up to 6 minutes costs $50

Over 6 and up to 15 minutes costs $80

Over 15 minutes costs $80 plus $5 per minute above 15 minutes

Which we can write like this:

function piecewise f(t)=50 if t<=6, 80 if t>6 and t<=15, 80 + 5(t-15) if t>15

You visit for 12 minutes, what is the fee? $80

You visit for 20 minutes, what is the fee? $80+$5(20-15) = $105

The Absolute Value Function

The Absolute Value Function is a famous Piecewise Function.

It has two pieces:

below zero: -x

from 0 onwards: x

Absolute Value function

f(x) = |x|

Absolute Value function

The Floor Function

The Floor Function is a very special piecewise function. It has an infinite number of pieces:

Floor function

The Floor Function

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OLEGan [10]
The temperature was -14°F at 8 a.m.

At noon is was 10 degrees warmer - the temperature increase was 10°F
-14°F + 10°F = -4°F

The tempertaure increase between noon and 4 p.m. was twice the previous increase in temperature, which was 10°F.
10°F x 2 = 20°F

We want to know the temperature at 4 p.m. so we just add it up to the previous result.
-4°F + 20°F = 16°F

16°F is the correct answer
4 0
3 years ago
Read 2 more answers
A curious patterns occurs in a group of people who all shake hands with one another. It turns out that you can predict the numbe
ycow [4]

Missing part of the question

Determine the number of handshakes, i, that will occur for each number of people, n, in a particular room. (people)

Answer:

S_n = \frac{n}{2}(n - 1)

Step-by-step explanation:

Given

For 5 people

\begin{array}{cc}{People} & {Handshakes} & {5} & {4} & {4} & {3} & {3} & {2} & {2} & {1} & {1} & {0} &{Total} & {10} \ \end{array}

Using the given instance of 5 people, the number of handshakes can be represented as:

(n - 1) + (n - 2) + (n - 3) + ........ + 3 + 2 + 1 + 0

The above sequence is an arithmetic sequence and the total number of handshakes is the sum of n terms of the sequence.

S_n = \frac{n}{2}{(T_1 + T_n})

Where

T_1 = n - 1 --- The first term

T_n = 0 --- The last term

So:

S_n = \frac{n}{2}(n - 1 + 0)

S_n = \frac{n}{2}(n - 1)

7 0
2 years ago
What is the lowest term of 75/60 as an improper fraction?
Katena32 [7]
75/60 = 15/12 = 5/4. This is the lowest term
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BRAINLIEST TO FIRST ANSWER
NNADVOKAT [17]

Answer:

The mean is 70, that's all I know. Sorry!

Step-by-step explanation:

Here's how you find the mean:

1. Add together ALL NUMBERS. (which equals 560 in this case.)

2. DIVIDE by the amount of numbers there are. (So 560 ÷ 8 = 70)

3. There's your answer! The mean of these numbers is 70.

I really hope this helps! Have a great day\night!

6 0
3 years ago
Solve the equation for x. show each step of the solution. name the justifications for each step of the solutions.
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9/2{8-x}+36=102-5/2{3x+24}
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96=12x you then divide and the answer obtained will be 8.
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