Geometry and Functions Exercises

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

The range of a function is the set of all possible output values (y-values) that the function can produce.

Determining the sign of a function means identifying whether the function's output values are positive, negative, or zero for different intervals of the input.

<p>To establish a variation table for a function, you need to find the critical points where the derivative changes sign. These critical points are often the roots of the derivative. Then, by examining the sign of the derivative in each interval determined by the critical points, you can determine whether the function is increasing or decreasing in that interval.</p> Signup and view all the answers

<p>The extremum of a function refers to its maximum or minimum values. These points occur where the derivative of the function is equal to zero or undefined.</p> Signup and view all the answers

<p>Giving the variation table of a function involves presenting the function's behavior in terms of intervals of increasing and decreasing values, based on the critical points where the derivative changes sign.</p> Signup and view all the answers

<p>Given the expression $f(x) = sin^{2}(x)$, we can visually determine the minimum by identifying the lowest points on the graph of the function. This would occur at the points where the sine function is equal to -1, which would result in $f(x) = 1$. So the minimum of the function $f(x) = sin^{2}(x)$ is 0.</p> Signup and view all the answers