QQuestionMathematics
QuestionMathematics
How do you find the domain and range without a graph?
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Step 1:: To find the domain of a function, we need to find all possible values of the input (usually x) for which the function is defined.
This means finding any restrictions on the input values.
Step 2:: Consider the function f(2$) = √(x - 3).
$$x - 3 \geq 0
The square root function is only defined for non-negative numbers, so we need to ensure that the expression inside the square root is greater than or equal to zero:
Step 3:: Solve this inequality to find the domain:
$$x \geq 3
So, the domain of the function is [3, ∞).
Step 4:: To find the range, we will use the fact that the square root function maps input values to their non-negative square roots.
Since x ≥ 3, the smallest possible value for x is 3, and the smallest possible value for √(x - 3) is therefore √(3 - 3) = 0.
Step 5:: As x increases, the value of √(x - 3) will also increase, approaching infinity as x approaches infinity.
Therefore, the range of the function is [0, ∞).
Final Answer
The domain of the function f(2$) = √(x - 3) is [3, ∞), and the range is [0, ∞).
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