Indicate which of the following four graphs is the correct graph of this function.

p(x)=(1/3)^2−x


Let's break down the function \( p(x) = \left( \frac{1}{3} \right)^2 - x \).

### Simplifying the expression:

1. First, simplify \( \left( \frac{1}{3} \right)^2 \):
   \[
   \left( \frac{1}{3} \right)^2 = \frac{1}{9}
   \]
   
2. The function becomes:
   \[
   p(x) = \frac{1}{9} - x
   \]

This is a linear function of the form \( p(x) = mx + b \), where \( m = -1 \) and \( b = \frac{1}{9} \).

### Characteristics of the graph:

- **Slope:** The slope \( m = -1 \) means that the graph decreases by 1 unit in \( p(x) \) for every 1 unit increase in \( x \). The line will slant downward from left to right.
  
- **Y-intercept:** The y-intercept is \( b = \frac{1}{9} \), meaning the line crosses the y-axis at \( \frac{1}{9} \).

### Conclusion:

The correct graph will be:
- A straight line,
- Sloping downwards with a slope of -1,
- Crossing the y-axis at \( \frac{1}{9} \).

If you have the graph options, you can match these characteristics to find the correct one.

Do you have any specific graphs you want to upload or ask about? Would you like further details?

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**Next questions to explore:**
1. How do we calculate slopes from graphs?
2. What does it mean for a function to be linear?
3. How would the graph change if the slope were positive?
4. How do vertical and horizontal shifts affect linear graphs?
5. What happens when the y-intercept is negative?

**Tip:** When identifying linear functions, remember that the slope defines how the line angles, while the y-intercept shows where it crosses the vertical axis.

Indicate which of the following four graphs is the correct graph of this function: p(x) = (1/3)^2 − x

Learn how to graph the linear function p(x) = (1/3)^2 − x, which simplifies to p(x) = 1/9 − x. Explore key concepts like slope, y-intercept, and how to recognize the correct graph. Suitable for students in Grades 7-10.

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