Question

based on the graph, which statement is true ? y = x + 2 (1,3) point of intersection y = 2x + 1 the point of intersection means that when x = 1 the two functions will have the same value of y which =3. the point of intersection means that when x = 3 the two functions will have the same value of y which =1. the point of intersection show the two functions are inverse. the two functions are equivalent.

Explanation:

Step1: Understand intersection concept

The point of intersection of two functions on a graph represents the values of \(x\) and \(y\) for which both functions have the same output (\(y - value\)).

Step2: Analyze given point

The point of intersection is \((1,3)\). This means when \(x = 1\), for \(y=x + 2\), \(y=1 + 2=3\); for \(y = 2x+1\), \(y=2\times1 + 1=3\).

Step3: Evaluate options

• Option 1: When \(x = 1\), \(y = 3\) for both functions. This is correct.
• Option 2: When \(x = 3\), for \(y=x + 2\), \(y=3+2 = 5\); for \(y=2x + 1\), \(y=2\times3+1=7\), so this is wrong.
• Option 3: To be inverse functions, their graphs should be symmetric about \(y = x\), which is not the case here, so this is wrong.
• Option 4: \(y=x + 2\) and \(y=2x + 1\) are not equivalent as \(x+2

eq2x + 1\) for all \(x\), so this is wrong.

Answer:

The point of intersection means that when \(x = 1\) the two functions will have the same value of \(y\) which \(=3\).