How do you find the domain and range of #10-x^2#?

Question

Nathan Axel · Accepted Answer

See below.

Examining a graph such as graph{10 - x^2 [-20, 20, -10, 10]} may be the most effective method for determining domain and range. The graph indicates that the maximum or highest point is located at (0,10), which is the y-intercept. As a result, you know that the range must be: y ≤ 10 The graph continues downward and across (left and right) until infinity, and you now want the domain. The domain is: (All real numbers) x = ℝ I hope that was helpful.

Nathan Axel · Answer

undefined To find the domain and range of the function $f(x) = 10 - x^2$, we need to consider the possible values of $x$ that the function can take and the corresponding values of $f(x)$.

1. **Domain**: The domain of a function is the set of all possible input values (values of $x$) for which the function is defined. Since $x$ can be any real number, the domain of $f(x) = 10 - x^2$ is all real numbers, which can be expressed as $(-∞, +∞)$.

2. **Range**: The range of a function is the set of all possible output values (values of $f(x)$) that the function can produce. For the function $f(x) = 10 - x^2$, the highest value that $f(x)$ can attain is $10$ when $x = 0$, and the function decreases as $x^2$ increases. Since $x^2$ can never be negative, the lowest value of $f(x)$ occurs when $x^2$ is at its maximum, which is $0$. Therefore, the range of $f(x) = 10 - x^2$ is $(-∞, 10]$.