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Ber [7]
3 years ago
8

The domain of f(x) is the set os all real numbers greater than or equal to 0 and less than or equal to 2. True of false

Mathematics
1 answer:
sveticcg [70]3 years ago
8 0

Answer:

True

Step-by-step explanation:

In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section, we will practice determining domains and ranges for specific functions. Keep in mind that, in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as tickets sales and year in the horror movie example above. We also need to consider what is mathematically permitted. For example, we cannot include any input value that leads us to take an even root of a negative number if the domain and range consist of real numbers. Or in a function expressed as a formula, we cannot include any input value in the domain that would lead us to divide by 0.

Diagram of how a function relates two relations.

Figure 2

We can visualize the domain as a “holding area” that contains “raw materials” for a “function machine” and the range as another “holding area” for the machine’s products.

We can write the domain and range in interval notation, which uses values within brackets to describe a set of numbers. In interval notation, we use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded. For example, if a person has $100 to spend, he or she would need to express the interval that is more than 0 and less than or equal to 100 and write

(

0

,

1

0

0

]

(0, 100]. We will discuss interval notation in greater detail later.

Let’s turn our attention to finding the domain of a function whose equation is provided. Oftentimes, finding the domain of such functions involves remembering three different forms. First, if the function has no denominator or an even root, consider whether the domain could be all real numbers. Second, if there is a denominator in the function’s equation, exclude values in the domain that force the denominator to be zero. Third, if there is an even root, consider excluding values that would make the radicand negative.

Before we begin, let us review the conventions of interval notation:

The smallest term from the interval is written first.

The largest term in the interval is written second, following a comma.

Parentheses, ( or ), are used to signify that an endpoint is not included, called exclusive.

Brackets, [ or ], are used to indicate that an endpoint is included, called inclusive.

The table below gives a summary of interval notation.

Summary of interval notation. Row 1, Inequality: x is greater than a. Interval notation: open parenthesis, a, infinity, close parenthesis. Row 2, Inequality: x is less than a. Interval notation: open parenthesis, negative infinity, a, close parenthesis. Row 3, Inequality x is greater than or equal to a. Interval notation: open bracket, a, infinity, close parenthesis. Row 4, Inequality: x less than or equal to a. Interval notation: open parenthesis, negative infinity, a, close bracket. Row 5, Inequality: a is less than x is less than b. Interval notation: open parenthesis, a, b, close parenthesis. Row 6, Inequality: a is less than or equal to x is less than b. Interval notation: Open bracket, a, b, close parenthesis. Row 7, Inequality: a is less than x is less than or equal to b. Interval notation: Open parenthesis, a, b, close bracket. Row 8, Inequality: a, less than or equal to x is less than or equal to b. Interval notation: open bracket, a, b, close bracket.

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Which expression is equivalent to 0.7×0.23
Marina CMI [18]
The answer is D because when multiplied by 1/10 you move the decimal place of 7 one space to the left so 7 now equals .7 and when multiplied by 1/100 23 is moved two spaces to the left to make .23
3 0
2 years ago
Read 2 more answers
La finca de Federico tiene tiene un área de 576 m2, En ella ha sembrado naranja y café, 3/8 de la finca están sembrados de naran
Vanyuwa [196]

Answer:

El área de la finca que está sembrada por café es 360 m².

Step-by-step explanation:

La finca de Federico tiene tiene un área de 576 m². \frac{3}{8} de la finca están sembrados de naranjas. Entonces, el área de la finca que está sembrada por naranjas se calcula mediante:

576 m²* \frac{3}{8} = 216 m²

Sabiendo que el resto de la finca esta sembrada de café, esta área se calcula mediante la diferencia del área total de la finca y el área sembrada por naranjas:

576 m² - 216 m²= 360 m²

<u><em>El área de la finca que está sembrada por café es 360 m².</em></u>

6 0
3 years ago
Out of students appeared in an examination 75% passed in English, 55%. passed in Mathematics, 5% failed in both subjects and 21
rusak2 [61]

Based on the percentage that passed English and those who passed Mathematics and those who failed and passed both, the total number of students who appeared in the examination are 60 students.

The number of students who passed only in Math are 12 students.

<h3>What number of students sat in the exam?</h3>

This can be found as:

= Total who passed English only + Total who passed Math only + Total who failed both + Total who passed both

Assuming the total is n, the equation becomes:

n = 0.75n - 21 + 0.55n - 21 + 21 + 0.05n

n = 1.35n - 21

21 = 0.35n

n = 21 / 0.35

= 60 students

The number who passed mathematics only is:

= (60 x 55%) - students who passed both

= 33 - 21

= 12 students

Find out more on Venn diagrams at brainly.com/question/24581814

#SPJ1

4 0
1 year ago
Solve the math problem please
koban [17]

Answer:

Option D

Step-by-step explanation:

Collect all like terms and Calculate

-10x-7x= -17x

20-54= -34

Divide

-17x < -34

x>2

6 0
3 years ago
Read 2 more answers
What is the area of triangle abc below? If necessary, round your answer to two decimal places..... PLEASE PLEASE HELP ME
antiseptic1488 [7]
For a triangle:
A=\frac{bh}{2}
A=\frac{b \times 7.9}{2}
b=AD+DC
Use Pythagorean theorem twice:
AD^{2}+9.4^{2}=7.9^{2}
AD=5.09

DC^{2}+23.2^{2}=7.9^{2}
DC=21.81

Thus:
b=26.9

And:
Area=\frac{26.9 \times 7.9}{2}=106.26

6 0
3 years ago
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