A linear function is given. Complete parts​ (a)-(d).
Upper G left parenthesis x right parenthesis equals 2

The given function is \( G(x) = 2 \). This represents a constant linear function, meaning that the output (or \( G(x) \)) is always 2, no matter the input value of \( x \). Now, let's complete the required parts step by step.

### (a) **Slope of the function**

The slope of a linear function is the rate of change of the function with respect to \( x \). Since the given function is constant (the value of \( G(x) \) doesn't change with \( x \)), the slope of this function is:

\[
\text{slope} = 0
\]

### (b) **Y-intercept of the function**

The y-intercept is the point where the function crosses the y-axis, which occurs when \( x = 0 \). For the function \( G(x) = 2 \), we can simply plug in \( x = 0 \):

\[
G(0) = 2
\]

Thus, the y-intercept is \( 2 \), and the corresponding point is \( (0, 2) \).

### (c) **Graph of the function**

The graph of this function is a horizontal line at \( G(x) = 2 \). This means that at any value of \( x \), the output will be 2. Therefore, the line is parallel to the x-axis and passes through the point \( (0, 2) \).

### (d) **Domain and Range**

- **Domain**: The domain of a function is the set of all possible input values. Since this is a constant function, the domain is all real numbers \( (-\infty, \infty) \).
  
- **Range**: The range is the set of all possible output values. In this case, the output is always 2, so the range is \( \{ 2 \} \).

### Summary:
- **Slope**: 0
- **Y-intercept**: \( (0, 2) \)
- **Graph**: A horizontal line at \( G(x) = 2 \)
- **Domain**: \( (-\infty, \infty) \)
- **Range**: \( \{ 2 \} \)

Would you like to see a visual graph or have further details?

Here are 5 related questions to deepen your understanding:
1. What would the graph look like if the function were \( G(x) = 3x + 2 \)?
2. How does the slope of a line affect its steepness?
3. Can a linear function have a negative slope? What would its graph look like?
4. What is the domain and range of the function \( G(x) = -4 \)?
5. How do you find the x-intercept of a linear function?

**Tip**: For any constant function \( f(x) = c \), the slope will always be 0, and the graph will be a horizontal line.

A linear function is given. Complete parts (a)-(d). G(x) = 2

Explore the linear function G(x) = 2, covering slope, y-intercept, domain, and range. This problem explains how the slope of a constant function is zero and how to graph horizontal lines. Suitable for students in Grades 6-8.

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