how the graph does the graph behave as x approaches positive or negative infinity. does it keep going at the same rate or does it approach a value but never touch it ?

The graph approaches positive infinity at a constant rate.The end behavior of this graph is:As x → -∞, f(x) → +∞For the first notation it looks at the behavior of the left side of the graph. As x approaches negative infinity (or positive xs) y or f(x) approaches positive infinity (or positive ys)andAs x → +∞, f(x) → +∞For the second notation it looks at the behavior of the right side of the graph. As x approaches positive infinity (or positive x's) y or f(x) approaches positive infinity (or positive ys)Hope this helped!~Just a girl in love with Shawn Mendes