Question

Can someone help me with this?

Answer 1

The function f(x) = -2 represents a constant linear function since the slope (m) is 0, indicating a horizontal line. The expression is simplified as f(x) = -2.

Given the values of x and f(x), we can determine whether f(x) represents a linear function. If it does, we can express it in the form f(x) = mx + b.

Let's calculate the slope (m) using two points, (-1, -2) and (2, -2):

`\[ m = \frac{\text{change in } y}{\text{change in } x} = (-2 - (-2))/(-1 - 2) = (0)/(-3) = 0 \]`

Since the slope (m) is 0, it indicates a constant function. Now, let's find the y-intercept (b) using any point, e.g., (0, -2):

`\[ f(0) = 0 \cdot m + b \]`

-2 = 0 + b

b = -2

Now, we can express f(x) in the form f(x) = mx + b:

`\[ f(x) = 0 \cdot x - 2 = -2 \]`

So, the correct choice is:

`\[ \text{A. } f(x) = -2 \]`