Final answer:
To find the domain of a function with a square root, set the expression under the square root ≥0 and solve for x; the range is typically from the lowest y-value to infinity. Use a calculator to perform square root operations, and solve equations by isolating and then squaring both sides to eliminate roots. Practice with different problems to build intuition for estimating reasonable answers.
Step-by-step explanation:
When dealing with functions that involve square roots, the domain will include all x-values for which the expression under the square root is non-negative, since square roots of negative numbers are not real. To find the domain of such a function, set the radicand (the expression under the square root) greater than or equal to zero, and solve for x.
For the range, it's helpful to visualize the function or consider its behavior. A function with a square root typically has a lower bound but no upper bound, so the range is often from some minimum y-value upwards to infinity. Remember that if the square root is part of a more complex expression, this can affect the range.
To determine a final answer, use your calculator to perform operations like finding square roots or inverse functions. You can also square the number and then take the square root to verify you understand these operations. Calculators often represent the square root function as a button with a radical sign (√) or using the power of 0.5, as any number raised to the 0.5 power is its square root. For equilibrium problems and equations involving square roots, solve carefully by isolating the square root and then squaring both sides of the equation to eliminate the root.
Understanding the domain and range is vital in avoiding mistakes and ensuring that your answers fall within a reasonable range. Practice with a variety of problems can enhance your intuition and ability to estimate reasonable answers.