let g(x)=x^2-8x+15/x^2-3x-10 and identify any asymptotes and point discontinuities of g(x) and graph the function and identify any x or y intercepts  

Here is the graph of \( g(x) = \frac{x - 3}{x + 2} \), showing the important features:

- **Vertical Asymptote** at \( x = -2 \) (dashed red line).
- **Horizontal Asymptote** at \( y = 1 \) (dashed green line).
- **x-Intercept** at \( (3, 0) \) (green dot).
- **y-Intercept** at \( \left(0, -\frac{3}{2}\right) \) (blue dot).
- **Point Discontinuity** at \( x = 5 \), where the function is undefined but marked with an open red circle.

Would you like further explanation on any specific part, or do you have questions?

Here are some related questions to deepen understanding:

1. How would the graph change if the numerator or denominator had a different degree?
2. What would happen if there was another removable discontinuity in the function?
3. How can you find the range of \( g(x) \) based on this graph?
4. What are the effects of changing the constants in \( g(x) \) on the asymptotes and intercepts?
5. How would you graphically interpret a slant asymptote in a rational function?

**Tip**: When simplifying rational functions, always check for removable discontinuities by factoring before canceling terms.

let g(x)=x^2-8x+15/x^2-3x-10 and identify any asymptotes and point discontinuities of g(x) and graph the function and identify any x or y intercepts

Explore the analysis of the rational function g(x) = (x^2 - 8x + 15) / (x^2 - 3x - 10), including identification of vertical and horizontal asymptotes, point discontinuities, and x- and y-intercepts. A detailed graph is provided along with step-by-step analysis for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation