Rational and Irrational Numbers Quiz

The number 0.5 is a rational number because it can be expressed as the fraction 1/2, where both the numerator and denominator are integers. It is not an integer or whole number.

The number \(\sqrt{3}\) cannot be expressed as a fraction of two integers, which defines a rational number. Since it is not possible to write \(\sqrt{3}\) in such a form, it is classified as an irrational number.

To find f(4), substitute x with 4 in the function f(x) = 3x + 2. This gives f(4) = 3(4) + 2 = 12 + 2 = 14. Therefore, the correct answer is 14.

The function f(x) = 1/x is undefined at x = 0, as division by zero is not possible. Therefore, the domain includes all real numbers except 0.

The relationship states that the total cost C is 5 times the number of items n. This can be expressed mathematically as C = 5n, which is the correct choice. The other options do not accurately represent this relationship.

The expression "the sum of a number x and 7" translates to adding 7 to x, which is represented as x + 7. Therefore, the correct choice is x + 7.

To solve for x in the equation x + 5 = 12, subtract 5 from both sides. This gives x = 12 - 5, which simplifies to x = 7. Therefore, the correct answer is 7.

The sum of two rational numbers can be expressed as a fraction, since rational numbers are defined as the ratio of two integers. Therefore, their sum is also a ratio of integers, making it rational.

To find g(2), substitute x with 2 in the function g(x) = 2x^2 - 3x + 1. This gives g(2) = 2(2)^2 - 3(2) + 1 = 8 - 6 + 1 = 3. Thus, the correct answer is 3.

The function f(x) = x^2 outputs values that are always greater than or equal to zero. Therefore, the range of the function is all non-negative numbers, which includes zero and all positive numbers.