2 Sketch the graph of h(x) of [ (x^2+5 x+6)/(x+1) ]

To sketch the graph of \( h(x) = \frac{x^2 + 5x + 6}{x + 1} \), we need to analyze the function's behavior, including its domain, intercepts, asymptotes, and general shape.### Step-by-Step Analysis:1. **Factor the Numerator:** So, the function simplifies to: 2. **Domain:** The function is undefined where the denominator is zero. Therefore, the domain is: 3. **Intercepts:** - **x-intercepts:** Set the numerator equal to zero: So, the x-intercepts are at and . - **y-intercept:** Set : So, the y-intercept is at .4. **Asymptotes:** - **Vertical Asymptote:** The function is undefined at , so there is a vertical asymptote at . - **Horizontal Asymptote:** For large values of , the term dominates, so: However, since the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. Instead, there is an oblique asymptote given by the quotient: 5. **Behavior Near Asymptotes:** - As , \( h(x) \to +\infty \). - As , \( h(x) \to -\infty \).6. **Plotting Points:** Choose a few points to plot the graph accurately: - : - : - : ### Graph Sketch:1. Draw the vertical asymptote at .2. Plot the x-intercepts at and .3. Plot the y-intercept at .4. Draw the oblique asymptote .5. Sketch the curve approaching the vertical asymptote as and the oblique asymptote as .Here is a rough sketch of the graph:```y|| /| /| /| /| /| /| /| /| /| / |/_________________________ x-3 -2 -1 0 1 2 3```In this sketch:- The vertical line at represents the vertical asymptote.- The line represents the oblique asymptote.- The points \( (-2,