Question

two functions are defined as shown.

\\(f(x) = -\frac{1}{2}x - 2\\)

\\(g(x) = -1\\)

which graph shows the input value for which \\(f(x) = g(x)\\)?

Explanation:

Set up the equation

We want to find the input value \(x\) where \(f(x) = g(x)\).
Using the System of Equations concept:

$$ -\frac{1}{2}x - 2 = -1 $$

Solve for x

Using the Linear Equations concept:

$$
LATEXBLOCK0
$$

Find the intersection point

Using the Graphical Intersection concept:
The intersection of \(f(x)\) and \(g(x)\) occurs at \((-2, -1)\).

Identify the correct graph

• Graph 1 (left): The lines intersect at \((2, -3)\).
• Graph 2 (middle): The lines intersect at \((-2, -1)\).
• Graph 3 (right): The lines intersect at \((2, -1)\).

Therefore, the middle graph is correct.

Answer:

• (A) Left graph (intersection at \((2, -3)\))
• (B) Middle graph (intersection at \((-2, -1)\)) (Correct answer)
• (C) Right graph (intersection at \((2, -1)\))