Finding the Range of a Function Graphed Below

As you continue to explore the world of mathematics, you will come across many functions that describe various phenomena. These functions can help you make sense of the world around you and solve complex real-life problems. The range of a function is one of the critical concepts that you must understand if you want to master these functions. In this article, we’ll discuss how to find the range of a function graphed below.

Before we delve into the details, it’s essential to understand what the range of a function is. Simply put, the range of a function is the set of all possible output values for a given input. In other words, it is the complete set of y-values that the function can produce. For example, suppose we have a function f(x) = x^2. The range of the function would be all non-negative real numbers since the square of any real number is non-negative.

Now let’s move on to finding the range of a function graphed below. When you’re given a graph, finding the range becomes a bit simpler. The range of a function graphed below is the set of all y-values that correspond to points on the graph. To find the range, examine the graph and identify the highest and lowest y-values. The range would be the set of all y-values between these two extremes.

To illustrate this concept, let’s consider the following function:

f(x) = 2x + 1

To find the range of this function, we need to graph it first. We can do this by creating a table of values and plotting the corresponding points on the Cartesian plane.

Table of values:
x | f(x)
-2 | -3
-1 | -1
0 | 1
1 | 3
2 | 5

Using these values, we can plot the points (-2, -3), (-1, -1), (0, 1), (1, 3), and (2, 5) on the Cartesian plane. We can then connect these points to get a straight line graph.

Now that we have graphed the function, we can find its range. From the graph, we can see that the lowest y-value is -3, and the highest y-value is 5. Therefore, the range of this function is the set of all y-values between -3 and 5, inclusive. We can write this as follows:

Range = {-3, -2, -1, 0, 1, 2, 3, 4, 5}

It’s essential to note that when finding the range of a function graphed below, you need to be careful not to exclude any possible y-values. You also need to ensure that you’ve identified all the extreme values correctly.

Another way to find the range of a function graphed below is by analyzing its behavior as x approaches infinity or negative infinity. If a function grows without bound, its range will also grow without bound. In contrast, if a function has a bounded range, it means that its output values are limited. For instance, let’s consider the following function:

f(x) = 1/x

If we graph this function, we can see that as x approaches zero, f(x) grows without bound. Therefore, the range of this function is all real numbers except 0. We can write this as follows:

Range = (-∞, 0) U (0, ∞)

In conclusion, finding the range of a function graphed below is an essential skill that every student of mathematics must learn. It involves identifying the highest and lowest y-values from the graph and including them in the range. Moreover, you can analyze the function’s behavior as x approaches infinity or negative infinity to find its range. With these tips in mind, you’ll be able to find the range of any function graphed below with ease.

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