Math Problem Statement

Given the equation y = (x - 1) / (x + 1), find the x-intercept and y-intercept.

Solution

I see that you've uploaded an image of a quiz review question. Let me transcribe and help you solve it.

From the image, the problem appears to be:

Given the equation y=x1x+1y = \frac{x-1}{x+1}, find the following:

  1. The x-intercept.
  2. The y-intercept.

Solution:

Let's solve this step by step.

1. Finding the x-intercept:

The x-intercept occurs where y=0y = 0. So, set the equation equal to zero:

0=x1x+10 = \frac{x-1}{x+1}

For the fraction to be zero, the numerator must be zero. So:

x1=0x - 1 = 0

x=1x = 1

Thus, the x-intercept is x=1x = 1.

2. Finding the y-intercept:

The y-intercept occurs where x=0x = 0. So, substitute x=0x = 0 into the equation:

y=010+1=11=1y = \frac{0 - 1}{0 + 1} = \frac{-1}{1} = -1

Thus, the y-intercept is y=1y = -1.

Final Answer:

  • x-intercept: x=1x = 1
  • y-intercept: y=1y = -1

Would you like further clarification or more details on this?

Here are 5 additional related questions to practice:

  1. How do you find the x-intercept of a quadratic equation?
  2. What happens to the intercepts if the equation is y=x+2x3y = \frac{x+2}{x-3}?
  3. How do you determine the vertical asymptotes of rational functions like this one?
  4. What is the domain of the function y=x1x+1y = \frac{x-1}{x+1}?
  5. How do the intercepts change if the function was y=2x3x+4y = \frac{2x-3}{x+4}?

Tip: To find the x-intercept of a function, always set y=0y = 0 and solve for xx.

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Math Problem Analysis

Mathematical Concepts

Algebra
Intercepts
Rational Functions

Formulas

x-intercept: Set y = 0 and solve for x
y-intercept: Set x = 0 and solve for y

Theorems

Basic principles of intercepts in algebra

Suitable Grade Level

Grades 9-12