Hva er funksjoner?

Definisjons- og verdimengde til en funksjon er mengdene av inngangs- og utgangsverdier for funksjonen. Denne videoen går i detalj for å forklare hvordan de fungerer.

To further explore the concept of domain and range, let's consider another example involving a quadratic function. Suppose we have the function $h(x)=x^2$. The graph of this function is a parabola that opens upwards. To determine the domain of $h$, we need to identify all possible x-values that can be input into the function. Since squaring any real number is always possible, the domain of $h$, denoted as $D_h$, is the set of all real numbers, $\mathbb{R}$.

Next, let's examine the range of $h$. The range consists of all possible y-values that the function can output. Observing the graph, we see that the parabola starts at the origin (0,0) and extends infinitely upwards. This means the smallest y-value is 0, and there is no upper limit. Therefore, the range of $h$, denoted as $R_h$, is the set of all non-negative real numbers, $[0,\infty )$. This example illustrates how the shape and direction of a graph can help us determine the domain and range of a function.