On a coordinate plane, a straight line has a positive slope. The formula for the line is f (x) = one-half x + 3. The line goes through points (negative 2, 2), (0, 3), and (2, 4). Which statements about the function f are true? Check all that apply. The domain of f(x) is {all real numbers}. The range of f(x) is {all real numbers}. The domain of f(x) is {x| x > 0}. The range of f(x) is {y| y > 0}. f(2) = 4 f(2) = 2(x + 3)
Answer (1)
Answer:The function f(x) = (1/2)x + 3 is a linear function with a positive slope, indicating that it is increasing across its domain. The domain of f(x) is all real numbers, as linear functions are defined for every real value of x. The range of f(x) is also all real numbers because as x approaches positive or negative infinity, y will also approach positive or negative infinity respectively. Therefore, the statements 'The domain of f(x) is {all real numbers}' and 'The range of f(x) is {all real numbers}' are true. The statement 'The domain of f(x) is {x | x > 0}' is false because the domain includes all real numbers, not just those greater than zero. Similarly, 'The range of f(x) is {y | y > 0}' is false because y can take any real value, including those less than or equal to zero. Evaluating the specific points: f(2) = (1/2)(2) + 3 = 1 + 3 = 4, so the statement 'f(2) = 4' is true. The statement 'f(2) = 2(x + 3)' is false because that would imply a different function; in fact, f(2) = (1/2)(2) + 3, not 2(x + 3).Step-by-step explanation:
