Quiz : How Much You Know About Trigonometric Domain & Range

1. The domain is the x-value in a problem.

True

False

The domain of a function refers to the set of all possible input values, which are represented by the x-values in a problem. It determines the values for which the function is defined and meaningful. Therefore, the statement that the domain is the x-value in a problem is true.

Explanation

The domain of a function refers to the set of all possible input values, which are represented by the x-values in a problem. It determines the values for which the function is defined and meaningful. Therefore, the statement that the domain is the x-value in a problem is true.

2. The range is the x-value in a problem.

True

False

The statement is false because the range is actually the set of all possible y-values in a problem, not the x-values. The x-values correspond to the domain of a function, while the y-values correspond to the range.

Explanation

The statement is false because the range is actually the set of all possible y-values in a problem, not the x-values. The x-values correspond to the domain of a function, while the y-values correspond to the range.

3. The independent variable is the output.

True

False

The statement is false because the independent variable is the variable that is manipulated or controlled by the researcher in an experiment. It is the variable that is believed to have an effect on the dependent variable, which is the output or the variable being measured. Therefore, the independent variable cannot be the output itself.

Explanation

The statement is false because the independent variable is the variable that is manipulated or controlled by the researcher in an experiment. It is the variable that is believed to have an effect on the dependent variable, which is the output or the variable being measured. Therefore, the independent variable cannot be the output itself.

4. The ______ is the same as the cause.

The term "domain" refers to a specific field or area of knowledge. In this context, the word "cause" implies that there is a reason or factor that leads to a certain outcome or effect. Therefore, the statement suggests that the domain, or field of knowledge, is equivalent to the cause, indicating that within a particular domain, one can identify the cause or reason behind a certain occurrence or phenomenon.

Explanation

The term "domain" refers to a specific field or area of knowledge. In this context, the word "cause" implies that there is a reason or factor that leads to a certain outcome or effect. Therefore, the statement suggests that the domain, or field of knowledge, is equivalent to the cause, indicating that within a particular domain, one can identify the cause or reason behind a certain occurrence or phenomenon.

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5. Find the domain of the point given(x, 4) when y= -8x+20.

0

2

4

6

The domain of a point in this context refers to the range of possible x-values that the point can have. In the equation y = -8x + 20, there are no restrictions on the x-values that can be plugged in. Therefore, the domain of the point (x, 4) is all real numbers, indicating that there are no limitations on the x-value.

Explanation

The domain of a point in this context refers to the range of possible x-values that the point can have. In the equation y = -8x + 20, there are no restrictions on the x-values that can be plugged in. Therefore, the domain of the point (x, 4) is all real numbers, indicating that there are no limitations on the x-value.

6. What are synonyms for the independent variable?

X, cause, output, domain

X, cause, input, domain

Y, cause, output, domain

Y, cause, input, domain

The independent variable is the variable that is manipulated or changed in an experiment. It is denoted by "x" in mathematical equations and represents the cause or input that is being studied. The other options, "y" and "output," are typically used to represent the dependent variable or the variable that is being measured or observed. Therefore, the correct synonyms for the independent variable are "x," "cause," "input," and "domain."

Explanation

The independent variable is the variable that is manipulated or changed in an experiment. It is denoted by "x" in mathematical equations and represents the cause or input that is being studied. The other options, "y" and "output," are typically used to represent the dependent variable or the variable that is being measured or observed. Therefore, the correct synonyms for the independent variable are "x," "cause," "input," and "domain."

7. The range is the independent variable.

True

False

The given statement is incorrect. The range is actually the dependent variable. In a mathematical function, the range represents the set of all possible output values for the corresponding input values from the domain. The independent variable is typically represented by the domain, which is the set of all possible input values for the function. Therefore, the range depends on the independent variable, making it the dependent variable.

Explanation

The given statement is incorrect. The range is actually the dependent variable. In a mathematical function, the range represents the set of all possible output values for the corresponding input values from the domain. The independent variable is typically represented by the domain, which is the set of all possible input values for the function. Therefore, the range depends on the independent variable, making it the dependent variable.

8. Find the range for the point given, (9,y), if y= -6x +63.

0

9

-9

117

The given equation is y = -6x + 63. To find the range for the point (9, y), we substitute x = 9 into the equation and solve for y.
y = -6(9) + 63
y = -54 + 63
y = 9
Therefore, the range for the point (9, y) is 9.

Explanation

The given equation is y = -6x + 63. To find the range for the point (9, y), we substitute x = 9 into the equation and solve for y.
y = -6(9) + 63
y = -54 + 63
y = 9
Therefore, the range for the point (9, y) is 9.

9. What are antonyms of an independent variable?

Output and y

Effect and range

Both answers

The antonyms of an independent variable are output and y, as well as effect and range. Antonyms are words that have opposite meanings. In this context, an independent variable is a factor that is manipulated or controlled in an experiment, while output, y, effect, and range are all related to the dependent variable, which is the variable being measured or observed. Therefore, these pairs of words can be considered as antonyms in the context of independent variables.

Explanation

The antonyms of an independent variable are output and y, as well as effect and range. Antonyms are words that have opposite meanings. In this context, an independent variable is a factor that is manipulated or controlled in an experiment, while output, y, effect, and range are all related to the dependent variable, which is the variable being measured or observed. Therefore, these pairs of words can be considered as antonyms in the context of independent variables.

10. Find the domain given the range 8,4 when y= 2x -8.

2

2, 6

8

0

The given equation is y = 2x - 8. To find the domain, we need to determine the possible values of x. Since there are no restrictions mentioned in the question, we can assume that x can take any real value. Therefore, the domain is all real numbers. The answer 2, 6 does not represent the domain, but rather the range of the equation when y is equal to 8 and 4 respectively.

Explanation

The given equation is y = 2x - 8. To find the domain, we need to determine the possible values of x. Since there are no restrictions mentioned in the question, we can assume that x can take any real value. Therefore, the domain is all real numbers. The answer 2, 6 does not represent the domain, but rather the range of the equation when y is equal to 8 and 4 respectively.