Science:Math Exam Resources/Courses/MATH110/December 2010/Question 09 (c)

MATH110 December 2010

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Question 09 (c)
Let $f(x)={\frac {x+1}{x-1}}$. Find all x- and y-intercepts of $\displaystyle f$, if they exist.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
What is the y-coordinate of an x-intercept? How about the x-coordinate of a y-intercept? Knowing this, how can you find the other coordinate of each kind of intercept?

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. The x-intercepts of $f(x)$ are all points of the form $(a,0)$, that is, all points where $y=0$. To find these x-values, we simply set the function $f(x)=0$ and solve for $x$. ${\begin{aligned}{\frac {x+1}{x-1}}&=0\\x+1&=0\\x&=-1\end{aligned}}$ So $f(x)$ has an x-intercept at $(-1,0)$. The y-intercept of $f(x)$ is the point of the form $(0,b)$, that is, where $x=0$. To find the y-intercept therefore, we simply plug $x=0$ into the function to find the y-value. $f(0)={\frac {0+1}{0-1}}={\frac {1}{-1}}=-1$ So the y-intercept is $(0,-1)$.

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