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The task asks to sketch the graph of the function \( f(x) = x^3 - 5 \). Here's a step-by-step explanation to help sketch this graph:

### Step 1: Understand the Function
The function \( f(x) = x^3 - 5 \) is a cubic function. Its general shape will resemble an \( x^3 \) curve but shifted vertically down by 5 units due to the \( -5 \).

### Step 2: Key Features
1. **Intercepts**:
   - **Y-intercept**: Set \( x = 0 \):
     \[
     f(0) = 0^3 - 5 = -5.
     \]
     The y-intercept is \( (0, -5) \).
   - **X-intercept**: Set \( f(x) = 0 \):
     \[
     x^3 - 5 = 0 \quad \Rightarrow \quad x^3 = 5 \quad \Rightarrow \quad x = \sqrt[3]{5}.
     \]
     Approximate \( x \approx 1.71 \).

2. **End Behavior**:
   - As \( x \to \infty \), \( f(x) \to \infty \).
   - As \( x \to -\infty \), \( f(x) \to -\infty \).

3. **Symmetry**:
   - The function is not symmetric because it is neither even nor odd.

### Step 3: Plot Points
Calculate several points to better sketch the curve:
   - \( f(-2) = (-2)^3 - 5 = -8 - 5 = -13 \).
   - \( f(-1) = (-1)^3 - 5 = -6 \).
   - \( f(0) = -5 \).
   - \( f(1) = 1^3 - 5 = -4 \).
   - \( f(2) = 2^3 - 5 = 8 - 5 = 3 \).

### Step 4: Sketch the Graph
1. Plot the calculated points \( (-2, -13), (-1, -6), (0, -5), (1, -4), (2, 3) \).
2. Draw a smooth curve passing through these points, keeping the end behavior and cubic shape in mind.

Would you like me to provide a detailed plot or clarify any of the steps? 

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### Questions for Practice:
1. How does the graph of \( f(x) = x^3 - 5 \) differ from \( f(x) = x^3 \)?
2. Find the slope of the tangent line to the curve at \( x = 2 \).
3. Determine whether \( f(x) = x^3 - 5 \) has any points of inflection.
4. What is the derivative of \( f(x) \), and how does it help in analyzing the curve?
5. Sketch \( f(x) = x^3 + 5 \) and compare it with \( f(x) = x^3 - 5 \).

### Tip:
For polynomial functions, always start by analyzing their intercepts, end behavior, and turning points to understand the overall graph shape.

Learn how to sketch the graph of the cubic function f(x) = x^3 - 5. This tutorial covers identifying intercepts, transformations, end behavior, and plotting key points for Grades 9-12.

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