Create a rational function with a linear binomial in both the numerator and denominator.

Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and intercepts.
Part 2. Show all work to identify the vertical asymptote, the x-intercepts, and the y-intercept.

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I can help you with that! However, rather than giving you the answer directly, I can guide you on how to solve it step by step. This way, you'll be able to understand the process and be able to solve similar problems in the future. Let's break it into two parts.

Part 1: Graphing the Rational Function
To graph the rational function, we need to consider the characteristics of the function such as asymptotes and intercepts. Here's how you can do that using technology (such as a graphing calculator or online graphing tool):

1. Start by choosing a linear binomial for both the numerator and denominator. Let's say we choose numerator (2x + 3) and denominator (x - 1).
f(x) = (2x + 3) / (x - 1)

2. Enter this function into a graphing tool or calculator of your choice.

3. The graphing tool should display the graph of the function. Look for the horizontal and vertical asymptotes. These are lines that the graph approaches but never touches.

4. Identify the x- and y-intercepts by looking for the points where the graph crosses the x- and y-axes.

5. Label the asymptotes and intercepts on the graph.

Part 2: Identifying Asymptotes and Intercepts
To identify the vertical asymptote, x-intercepts, and y-intercept, we need to do some algebraic work. Here's how you can do that:

1. Consider the rational function f(x) = (2x + 3) / (x - 1) that we used in Part 1.

2. Vertical Asymptote: To find the vertical asymptote, set the denominator equal to zero and solve for x. In this case, (x - 1) = 0 gives x = 1. So, the vertical asymptote is x = 1.

3. X-intercepts: To find the x-intercepts, set the numerator equal to zero and solve for x. Here, (2x + 3) = 0 gives x = -3/2. So, the x-intercept is (-3/2, 0).

4. Y-intercept: To find the y-intercept, substitute x = 0 into the rational function and solve for y. In this case, (2(0) + 3) / (0 - 1) gives y = -3.

By following these steps, you will be able to create and graph a rational function with linear binomials, and also find the vertical asymptote, x-intercepts, and y-intercept.

I cannot provide a graph since I am a text-based AI and do not have the ability to display visual images. However, I can guide you through the process of creating the rational function and finding its asymptotes and intercepts.

Part 1: Graphing the function
1. Choose a linear binomial for the numerator and denominator. Let's use (3x + 2) for both the numerator and denominator.
2. Write the rational function as follows:
f(x) = (3x + 2) / (3x + 2)
Notice that the numerator and denominator are the same. This will result in a simplified rational function with a horizontal asymptote at y = 1.

Part 2: Identifying the asymptotes and intercepts
1. Vertical Asymptote:
To identify the vertical asymptote, set the denominator equal to zero and solve:
3x + 2 = 0
3x = -2
x = -2/3
Therefore, the vertical asymptote is x = -2/3.

2. X-Intercepts:
To find the x-intercepts, set the numerator equal to zero and solve:
3x + 2 = 0
3x = -2
x = -2/3
So the x-intercept is (-2/3, 0).

3. Y-Intercept:
To find the y-intercept, substitute x = 0 into the rational function:
f(0) = (3(0) + 2) / (3(0) + 2)
f(0) = 2/2
f(0) = 1
So the y-intercept is (0, 1).

Now, you can graph the function using the identified asymptotes and intercepts.