1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
valentinak56 [21]
3 years ago
6

A function f is​ _____ on an open interval I​ if, for any choice of x1 and x2 in​ I, with 1 less than

Mathematics
1 answer:
Zepler [3.9K]3 years ago
3 0

Answer:

If f(x_1)\leq f(x_2) whenever x_1\leq x_2 f is <em>increasing</em> on I.

If f(x_1)\geq f(x_2) whenever x_1\leq x_2 f is <em>decreasing</em> on I.

Step-by-step explanation:

These are definitions for real-valued functions f:I→R. To help you remember the definitions, you can interpret them in the following way:

When you choose any two numbers x_1\leq x_2 on I and compare their image under f, the following can happen.

  • f(x_1)\leq f(x_2). Because x2 is bigger than x1, you can think of f also becoming bigger, that is, f is increasing. The bigger the number x2, the bigger f becomes.
  • f(x_1)\geq f(x_2). The bigger the number x2, the smaller f becomes so f is "going down", that is, f is decreasing.

Note that this must hold for ALL choices of x1, x2. There exist many functions that are neither increasing nor decreasing, but usually some definition applies for continuous functions on a small enough interval I.

You might be interested in
Can someone help me with math
Tresset [83]
I want to say 7.6% is the answer
6 0
3 years ago
Read 2 more answers
Can someone SMART redo these questions I mean I made a seven and I did all I could I need to know what went wrong
adoni [48]
2. 8x -28 = -140
8x -28 + 28 = -140 + 28
8x = -112
8x/8 = -112/8
x = -14

3. -9 + x/3 = -23
-9 + 9 + x/3 = -23 + 9
x/3 = -14
x/3/3 = -14/3
x = -14/3

4. x/-1.5 - 3.5 = -13.5
x/-1.5 - 3.5 + 3.5 = -13.5 + 3.5
x/1.5 = -10
x/-1.5/-1.5= -10/-1.5
x = 20/3

5.-6(x + 3) = -36
-6x - 18 = -36
-6x - 18 + 18 = -36 + 18
-6x = -18
-6x/-6 = -18/-6
x = 3

6. k + 3.7/9.8 = -0.22
k + 3.7/9.8/9.8 = -0.22/9.8
k + 3.7 = -2.156
k + 3.7 - 3.7 = -2.156 - 3.7
k = -5.856

7. 12(x - 6) = -108
12x - 72 = -108
12x - 72 + 72 = -108 + 72
12x = -36
12x/12 = -36/12
x = -3

8. -21.83x - -19.9 = -23.83
-21.83x + 19.9 = -23.83
-21.83x + 19.9 - 19.9 = -23.83 - 19.9
-21.83x = -43.73
-21.83x/-21.83 = -43.73/-21.83
x = 2

9. -10x - 68 + x = 40
-9x - 68 = 40
-9x -68 + 68 = 40 + 68
-9x = 108
-9x/-9 = 108/-9
x = -12

10. -34 - 3x - 2x = 71
-34 - 5x = 71
-34 + 34 - 5x = 71 + 34
-5x = 105
-5x/-5 = 105/-5
x = -21

11. 3x - 77 - 8x = 23
-5x - 77 = 23
-5x - 77 + 77 = 23 + 77
-5x = 100
-5x/-5 = 100/-5
x = -20

12. 3x - 5(2x - 12) = 123
3x - 10x + 60 = 123
-7x + 60 = 123
-7x + 60 - 60 = 123 - 60
-7x = 63
-7x/-7 = 63/-7
x = -9

13. -3x + 6(x + 6) = 15
-3x + 6x + 36 = 15
3x + 36 = 15
3x + 36 - 36 = 15 - 36
3x = -21
3x /3 = -21/3
x = -7

14. 5x + 2(4x - 9) = -174
5x + 8x - 18 = -174
13x - 18 = -174
13x - 18 + 18 = -174 + 18
13x = -156
13x/13 = -156/13
x = -12

15. -3x + 6(5x + 3) = -171
-3x + 30x + 18 = -171
27x + 18 = -171
27x + 18 - 18 = -171 - 18
27x = -189
27x/27 = -189/27
x = -7










5 0
3 years ago
(-4)= ? a. -4 B. 4 C.0 d. none above
Anit [1.1K]
If it’s just (-4) with nothing in front the answer is -4
3 0
2 years ago
What is the unit rate 2y=9x
beks73 [17]
9/2 that the answer ok ok 

3 0
4 years ago
Read 2 more answers
If rectangle ABCD is translated 5 units right and 3 units down, what are the coordinates of A'.
alexandr402 [8]

The coordinated of A would be 1,1.
Instead of going through the trouble of mentally moving the entire thing, just focus on the one you need to know the answer to, aka A.  

3 0
2 years ago
Read 2 more answers
Other questions:
  • Tyler wants to buy a bike that cost 125 he has already saved 110 he earns 8 dollars a hour as a lifeguard he saves all of it for
    15·1 answer
  • NEED HELP ASAP WILL MARK BRAINLIEST
    11·1 answer
  • Write the value of the 6 in 106,534
    11·2 answers
  • The measure of the supplement of a 129 degree angle
    9·2 answers
  • The school band sold T-shirts to raise money for an upcoming trip. It sold 120 shirts, which was 30 percent of the total sales o
    9·2 answers
  • The scale on the architectural plans for a new house is 1 in. equals 4 ft. Find the length and width (in ft) of a room that meas
    12·1 answer
  • Determine the domain of (f/g) (x) when f(x)=1/x and g(x)= sqrt x+5
    5·2 answers
  • PLZ HELP ASAP WILL GIVE BRAINLEIST
    5·2 answers
  • o figure out a special number, Tammi’s mother was supposed to double her age and then add 4. Instead, Tammi’s mother added 4 to
    8·2 answers
  • Can somebody help me?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!