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.
I am a mom and my student is homeschooled. She is asking me for help on her final assessment and I am completely lost. Can anyone explain with answer?
She is homeschooled through Florida Virtual School because she is a dancer and could not handle regular school. She did not have time. You are being very unprofessional. Do not be so ignorant. And I do not think any children should be learning from your explanation if you do not even know the difference between were and where. Thank you. Have a nice night.
Why are people judging this mom. If she wants to dance and can't go to school then leave her alone. Reiny don't be rude.
At least she's getting an education, I used to be a dancer and its definitely time consuming but its worth it. And as long as she's getting an education theres nothing wrong with how she's getting it. And whatever she does is none of your business therefore you have no reason to be so narrow-minded.
Of course! I can help you with that. Let's start by understanding what a rational function is. A rational function is a function that can be written as the ratio of two polynomial functions. In simpler terms, it is a fraction where both the numerator and denominator are polynomials.
For this exercise, we need to create a rational function with a linear binomial in both the numerator and denominator. Let's start by considering a linear binomial in the numerator, such as (2x + 3), and another linear binomial in the denominator, such as (x - 1).
So our rational function will look like this:
f(x) = (2x + 3) / (x - 1)
Now, let's move on to graphing the function using technology. You can use a graphing calculator or an online graphing tool to easily plot the graph. The graph will help us locate the asymptotes and intercepts.
To find the graph, we first plug the rational function into a graphing tool. Here is an example graph of the function:
Graph of f(x) = (2x + 3) / (x - 1)
Horizontal Asymptote:
To find the horizontal asymptote of the graph, we look at the degrees of the numerator and the denominator.
Since the degree of the numerator (1) is less than the degree of the denominator (1), the horizontal asymptote is y = 0 (the x-axis).
Vertical Asymptote:
To find the vertical asymptotes, we set the denominator (x - 1) equal to zero and solve for x. In this case, x = 1. Therefore, x = 1 is the vertical asymptote.
X-intercepts:
To find the x-intercept, we set the numerator (2x + 3) equal to zero and solve for x. In this case, there is no x-intercept since the equation 2x + 3 = 0 has no real solutions.
Y-intercept:
To find the y-intercept, we substitute x = 0 into the equation f(x). In this case, f(0) = (2*0 + 3) / (0 - 1) = 3 / -1 = -3. Therefore, the y-intercept is (0, -3).
Now, let's summarize the findings:
- Horizontal Asymptote: y = 0 (x-axis)
- Vertical Asymptote: x = 1
- X-intercepts: None
- Y-intercept: (0, -3)
I hope this explanation helps you and your student. Feel free to ask if you have any further questions!
Amen!
You sure got me on that "were" vs "where".
As to education vs dancing, you are absolutely free to set your priorities.
Sorry to say this, but if you are homeschooling your child and you are "completely lost" with this routine question, perhaps it is time to send him/her to a regular school were qualified math teachers can do it.
both Steve and I have both answered this question, using a different example each time.
Steve's :
http://www.jiskha.com/display.cgi?id=1465520203
Mine:
http://www.jiskha.com/display.cgi?id=1465517106