example 1\nfind the following:\ndomain\nrange\nx intercept\ny intercept\nintervals\n increasing\n…

Explanation:

Domain

The domain of a function is the set of all possible (x) - values. Since the graph extends infinitely to the left and right (as indicated by the arrows), the domain is ((-\infty,\infty)).

Range

The range is the set of all possible (y) - values. Looking at the graph, the (y) - values go from (-\infty) up to a maximum (y) - value of approximately (2). So the range is ((-\infty, 2]).

(x) - intercept

The (x) - intercept is the point where (y = 0). From the graph, this occurs at (x = 0).

(y) - intercept

The (y) - intercept is the point where (x = 0). From the graph, when (x = 0), (y=0).

Intervals of Increase

A function is increasing when the slope is positive. Looking at the graph, it is increasing on the interval ((-1,1)).

Intervals of Decrease

A function is decreasing when the slope is negative. The graph is decreasing on ((-\infty,-1)\cup(1,\infty)).

Intervals of Constant

There are no intervals where the function is constant (i.e., slope ( = 0) over an interval, not just at a point).

Relative Maximum

A relative maximum is a point where the function changes from increasing to decreasing. At (x = 1), (y = 2). So the relative maximum is ((1,2)).

Relative Minimum

A relative minimum is a point where the function changes from decreasing to increasing. At (x=-1), (y=-2). So the relative minimum is ((-1,-2)).

Answer:

• Domain: ((-\infty,\infty))
• Range: ((-\infty, 2])
• (x) - intercept: ((0,0))
• (y) - intercept: ((0,0))
• Increasing: ((-1,1))
• Decreasing: ((-\infty,-1)\cup(1,\infty))
• Constant: None
• Relative Maximum: ((1,2))
• Relative Minimum: ((-1,-2))