Please help me solve with work shown **Graphing Rational Functions: A Step-by-Step Guide****Problem:**7. Graph \( y = \frac{x^2 + 3x - 10}{x - 1} \). You must clearly and accurately label the locations of all intercepts, asymptotes (including oblique), and places where the graph crosses asymptotes.**Solution:**To accurately graph the function \( y = \frac{x^2 + 3x - 10}{x - 1} \), follow these steps:1. **Factor the Numerator (if possible):** \( x^2 + 3x - 10 = (x + 5)(x - 2) \) So, \( y = \frac{(x + 5)(x - 2)}{x - 1} \).2. **Find the Intercepts:** - **X-Intercepts:** Set \( y = 0 \): \( 0 = \frac{(x + 5)(x - 2)}{x - 1} \) Thus, \( x + 5 = 0 \) or \( x - 2 = 0 \) X-intercepts are at \( x = -5 \) and \( x = 2 \). - **Y-Intercepts:** Set \( x = 0 \): \( y = \frac{(0 + 5)(0 - 2)}{0 - 1} = \frac{-10}{-1} = 10 \) Y-intercept is at (0, 10).3. **Find the Asymptotes:** - **Vertical Asymptote:** Set the denominator equal to zero: \( x - 1 = 0 \) Vertical asymptote at \( x = 1 \). - **Horizontal Asymptote:** Consider the degrees of the numerator and denominator. Since the degree of the numerator is one more than the degree of the denominator, there's no horizontal asymptote but an oblique (slant) asymptote. - **Oblique Asymptote:** Perform polynomial long division: Divide \( x^2 + 3x - 10 \) by \( x - 1 \). The quotient is \( x + 4 \), so the oblique asymptote is \( y =

Name: Please help me solve with work shown **Graphing Rational Functions: A
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please help me solve with work shown **Graphing Rational Functions: A Step-by-Step Guide****Problem:**7. Graph \( y = \frac{x^2 + 3x - 10}{x - 1} \). You must clearly and accurately label the locations of all intercepts, asymptotes (including oblique