The image provides two rational functions that need to be graphed on the given coordinate grids.

Problem 7:

$y = \frac{x + 3}{x - 2}$

• Vertical asymptote: This occurs where the denominator equals zero, so set $x - 2 = 0$, which gives $x = 2$.
• Horizontal asymptote: Since the degrees of the numerator and denominator are the same (both degree 1), the horizontal asymptote is found by dividing the leading coefficients, which gives $y = 1$.
• X-intercept: Set the numerator equal to zero, $x + 3 = 0$, so $x = -3$.
• Y-intercept: Set $x = 0$ in the function: $y = \frac{0 + 3}{0 - 2} = -\frac{3}{2}$ Thus, the y-intercept is $y = -1.5$.

Problem 8:

$y = \frac{x^2 + 2x - 3}{x - 1}$

• Vertical asymptote: This occurs where the denominator equals zero, so set $x - 1 = 0$, which gives $x = 1$.
• Slant asymptote: Since the degree of the numerator is one higher than the denominator, there is no horizontal asymptote, but a slant asymptote can be found by performing polynomial division of $x^2 + 2x - 3$ by $x - 1$. The result is $y = x + 3$.
• X-intercepts: Set the numerator equal to zero and solve $x^2 + 2x - 3 = 0$. Factoring gives $(x + 3)(x - 1) = 0$, so $x = -3$ and $x = 1$ (but we exclude $x = 1$ because it's also the location of the vertical asymptote).
• Y-intercept: Set $x = 0$ in the function: $y = \frac{0^2 + 2(0) - 3}{0 - 1} = \frac{-3}{-1} = 3$ Thus, the y-intercept is $y = 3$.

Would you like a detailed explanation on how to graph these functions, or more information on how the asymptotes affect the graph?

Related questions:

1. How do you identify vertical asymptotes in a rational function?
2. What are the conditions for having a slant asymptote?
3. How do you calculate the x-intercepts of a rational function?
4. How does the degree of a rational function affect its horizontal asymptote?
5. What role do intercepts play in shaping the graph of a rational function?

Tip: When graphing rational functions, always start by determining the asymptotes and intercepts. These features give you key points and structure to sketch the curve.