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**Transcription of the visible content:**

1. **Graphical Representation**  
   \( f(x) = \begin{cases} 
   x+1 & \text{if } x \leq 1 \\
   x^2-1 & \text{if } x > 1 
   \end{cases} \)

   - Determine \( f(1.5) \).
   - Sketch the graph of \( f(x) \).

2. **Values of x for which**  
   \[ x^2 + 5x - 6 = 0 \]

3. **Determine the limit of the function**  
   \[
   \lim_{x \to 1} \frac{x^3 - 1}{x - 1}
   \]

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### Let's go through these one by one:

1. **Determine \( f(1.5) \)**:  
   The piecewise function is defined as:
   \[
   f(x) = 
   \begin{cases} 
   x+1 & \text{if } x \leq 1 \\
   x^2-1 & \text{if } x > 1 
   \end{cases}
   \]
   Since \( 1.5 > 1 \), use the second condition:
   \[
   f(1.5) = (1.5)^2 - 1 = 2.25 - 1 = 1.25
   \]

2. **Sketch the graph of \( f(x) \)**:
   - For \( x \leq 1 \): \( f(x) = x + 1 \), which is a straight line with slope 1, intersecting the y-axis at \( y = 1 \).
   - For \( x > 1 \): \( f(x) = x^2 - 1 \), which is a parabolic curve opening upwards, shifted down by 1 unit.

3. **Solve \( x^2 + 5x - 6 = 0 \)**:  
   This is a quadratic equation. We can factorize it:
   \[
   x^2 + 

Graphical Representation of a piecewise function and solving quadratic equations.

Explore the detailed solutions for piecewise functions, quadratic equations, and limit calculations. Understand how to graph piecewise functions and solve quadratic equations, suitable for students in Grades 10-12.

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