The function g (x) = 2x -1 can be graphically represented by a line with positive slope. By examining the graph, it is clear that g (x) always increases. We can also show this using the definition of increasing function. Let x₂ > x₁. Then we have,

x₂ > x₁,

2x₂ > 2x₁, 

2x₂ -1 > 2x₁ -1, 

g (x₂) > g (x₁).

We have shown g (x) always increases becauseg (x₂) > g (x₁) whenever x₂ > x₁.

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