Domain: All real numbers such that 3x + 4 ≥ 0 (to ensure that the square root is valid), so x ≥ -4/3.
Range: All real numbers, since the square root can result in any non-negative number.
What are the domain and range of the function y equals 2 (square root 3x plus 4 )minus 5
5 answers
what is range
To find the exact range of the function, we need to consider the properties of the square root function and how it affects the output of the function.
The square root function always produces non-negative values. In this case, we have y = 2√(3x + 4) - 5.
To determine the range, we need to analyze how the values of x affect the output of the function. As x varies, the square root term (3x + 4) can only produce non-negative values. Multiplying by 2 and subtracting 5 further affects these values.
Since the square root term always produces non-negative values and the function further modifies these values, the range of the function y = 2√(3x + 4) - 5 is all real numbers ( -∞ < y < ∞).
The square root function always produces non-negative values. In this case, we have y = 2√(3x + 4) - 5.
To determine the range, we need to analyze how the values of x affect the output of the function. As x varies, the square root term (3x + 4) can only produce non-negative values. Multiplying by 2 and subtracting 5 further affects these values.
Since the square root term always produces non-negative values and the function further modifies these values, the range of the function y = 2√(3x + 4) - 5 is all real numbers ( -∞ < y < ∞).
what are real number
In mathematics, real numbers include all the rational and irrational numbers on the number line. Real numbers can be positive, negative, or zero. They can be represented as points on an infinitely extending line known as the real number line.
Examples of real numbers include:
- Integers (both positive and negative whole numbers)
- Fractions (or rational numbers)
- Irrational numbers (such as the square root of 2 or pi)
- Decimal numbers
In short, real numbers encompass a wide range of numbers, both rational and irrational, that can be represented on the number line.
Examples of real numbers include:
- Integers (both positive and negative whole numbers)
- Fractions (or rational numbers)
- Irrational numbers (such as the square root of 2 or pi)
- Decimal numbers
In short, real numbers encompass a wide range of numbers, both rational and irrational, that can be represented on the number line.