How to tell if the domain is all real numbers

Asked by admin @ in Mathematics viewed by 373 People

Find the domain and range of the relation and determine whether it is a function.

a. domain: all real numbers; range: all real numbers; Yes, it is a function.
b. domain: positive integers; range: positive integers; No, it is not a function.
c. domain: x ≥ 0; range: y > 3; No, it is not a function.
d. domain: x > 3; range: y > 0; Yes, it is a function.

Answered by admin @


Using function concepts, it is found that the correct option is:

d. domain: x > 3; range: y > 0; Yes, it is a function.

A relation is a function if for each value of the input, there is only one respective value of the output. In a graph, it means that for each value of x, there is only one respective value of y.

  • In this graph, there is only one value of y for each value of x, hence, it is a function.

The domain of a function is the set that contains all possible input values. In a graph, it is the values assumed by x, the horizontal axis.

  • In this graph, x assumes values greater than 3, hence the domain is x > 3.

The range of a function is the set that contains all possible output values. In a graph, it is the values assumed by y, the vertical axis.

  • In this graph, y assumes values greater than 0, hence the range is y > 0.

A similar problem is given at brainly.com/question/10891721


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