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Usimov [2.4K]
3 years ago
6

In 2.2, recall that on an open interval, the end points are not included in the interval. For example, the open interval (2, 4)

represents the real numbers between, but not including, 2 and 4. In a closed interval, the end points are included in the interval. For example, the closed interval [5,8] represents the real numbers between and including, 5 and 8. In some text books (including ours), they define increasing, decreasing, and constant on open intervals. Other texts do not require the intervals to be open, meaning they can be defined on closed intervals. What do you think? Should increasing, decreasing, and constant intervals be defined on open intervals or do you think they should be defined on closed intervals? Why?​
Mathematics
1 answer:
spayn [35]3 years ago
6 0

9514 1404 393

Answer:

  it depends

Step-by-step explanation:

The ideas of "increasing" or "decreasing" have to do with the sign of the derivative of a function. The derivative of a function is a limit, which is only defined if the point can be approached from both sides. For a function that is only defined on an interval, the derivative is undefined (hence "increasing" or "decreasing" are undefined) at the end points of the interval.

When the function is defined on an interval, "increasing" or "decreasing" can only be determined on that open interval. There may also be critical points within an interval at which the derivative is either zero or undefined. Those points must also be excluded from any interval of "increasing" or "decreasing".

__

If a function is defined over a domain that extends beyond the interval of interest, then the derivative may very wll be defined a the end points of the interval of interest. As a simple example, consider a line with defined non-zero slope: y = kx, k≠0. For k>0, the line will be increasing everywhere. The slope is defined at the end points of any finite interval, so the function can be said to be "increasing" on the closed interval.

Similarly, if the (finite) interval of interest includes the vertex of a parabola defined for all real numbers, the function will be "increasing" on one side of the vertex, and "decreasing" on the other side. Both the "increasing" and "decreasing" intervals will be half-open intervals. The point at the vertex will not be included in either of them.

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Which statement best illustrates using the vertical line test to determine if the graph below is a function of x ?
kirill115 [55]

If something is a function, every x-value, only has one (1) y-value. If the line x = 0 intersects the graph in two points, there are to values for y (instead of one). Therefore the graph is not a function of x.


Your answer is A.


4 0
3 years ago
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Rooter Plus charges a $25 service fee plus $40 per hour of work done. Is this a proportional or non-proportional relationship?
Dominik [7]

Answer:

Non-proportional; the rate of change is $40/hour

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=k or y=kx

In a proportional relationship the constant of proportionality k is equal to the slope m of the line <u>and the line passes through the origin</u>

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x -----> the number of hours

y ----> The total charge in dollars

The equation of the line in slope intercept form is equal to

y=mx+b

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y=40x+25

This relationship is not proportional, because the line not passes through the origin

therefore

Non-proportional; the rate of change is $40/hour

5 0
3 years ago
A number y multiplied by −3 is less than −2/5. Write this word sentence as an inequality.
bazaltina [42]
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8 0
3 years ago
PLEASE HELP ME ( I ADDED A PHOTO)
Nostrana [21]

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Which one do you need help with

Step-by-step explanation:

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4 0
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Question 5 of 10
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Answer:

x= 38

Step-by-step explanation:

add 34 to each side of the equation.

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done!

5 0
2 years ago
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