Question

which input value produces the same output value for the two functions on the graph? \\(\circ\\) \\(x = -1\\) \\(\circ\\) \\(x = 0\\) \\(\circ\\) \\(x = 1\\) \\(\circ\\) \\(x = 2\\)

Explanation:

Step1: Recall Intersection Meaning

The input value (x) that produces the same output (y) for two functions is the x - coordinate of their intersection point.

Step2: Identify Intersection Point

Looking at the graph, the two lines \( f(x) \) (red) and \( g(x) \) (blue) intersect at the point where \( x = 1 \) (and \( y = 1 \)). We can check the options:

• For \( x=-1 \): The two functions have different y - values.
• For \( x = 0 \): The two functions have different y - values.
• For \( x = 1 \): The two functions meet at this x - value, so they have the same output.
• For \( x = 2 \): The two functions have different y - values.

Answer:

\( \boldsymbol{x = 1} \) (corresponding to the option "x = 1")