The range of f(x) = ax + b is the set of all real numbers given that a and b are real numbers. Which produces a counter example to her statement?
To produce a counterexample to the claim that the range of f(x) = ax + b is the set of all real numbers when a and b are real numbers, we need to find specific values for a and b where the range is not all real numbers.
Let's consider the case where a = 0 and b ≠ 0. In this situation, the function becomes f(x) = 0x + b = b. The range of this function is a single value, which is b. Therefore, it is not the set of all real numbers unless b = ∞ (infinity).
Hence, a = 0 and b ≠ 0 provide a counterexample to the claim that the range of f(x) is the set of all real numbers.
To find a counter example, we need to find specific values for a and b such that the range of f(x) = ax + b is not the set of all real numbers.
Let's assume a = 0 and b = 1. In this case, the equation becomes f(x) = 0x + 1 = 1. The range of this function is a constant value, 1. Therefore, the range is not the set of all real numbers, as the function only produces the real number 1.
Hence, the values a = 0 and b = 1 provide a counter example, as they do not result in the range being the set of all real numbers.