I am having to explain how to find the domain and range of a rational function from its graph.
Can someone help me to try and put this into simple terms.
the domain is your choice of x's you can use in the equation.
the range is the resulting y's obtained by using those x's
Certainly! Finding the domain and range of a rational function from its graph involves a few steps:
1. Start by identifying the x-values that are not included in the graph (any vertical asymptotes or holes). These values are restricted because they would result in division by zero, which is undefined. The union of these restricted values gives you the domain of the function.
2. Next, examine the y-values of the graph. Determine the lowest and highest points on the graph. The set of all y-values between or including these extreme points represents the range of the function.
To explain this process more simply:
1. Look for any values of x that would make the function "break," such as points where the graph has vertical lines or holes. These values are not part of the domain.
2. Find the highest and lowest points on the graph. The range consists of all the y-values between or including these points.
Remember, the domain represents all the valid x-values, while the range represents the corresponding y-values.