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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.

Graph each rational function. Problem 7: y = (x + 3) / (x - 2) and Problem 8: y = (x^2 + 2x - 3) / (x - 1).

Learn how to graph the rational functions y = (x + 3) / (x - 2) and y = (x^2 + 2x - 3) / (x - 1). This problem covers key concepts like vertical and slant asymptotes, and how to find intercepts. Suitable for high school students in Grades 9-12.

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