example 5 find the following: domain range x intercept y intercept intervals increasing decreasing constant…

Explanation:

Domain

The domain of a function is the set of all possible (x) - values. Looking at the graph, the left - most point is at (x=-4) and the graph extends to the right without bound. So, the domain is ([-4,\infty)).

Range

The range is the set of all possible (y) - values. The lowest (y) - value (at (x = - 4)) is (y = 1) and the graph extends upwards without bound. So, the range is ([1,\infty)).

(x) - intercept

The (x) - intercept is the value of (x) when (y = 0). From the graph, there is no point where (y = 0). So, there is no (x) - intercept.

(y) - intercept

The (y) - intercept is the value of (y) when (x = 0). Looking at the graph, when (x = 0), (y\approx2.5).

Intervals of Increase, Decrease, and Constant

• Increasing: A function is increasing if, as (x) increases, (y) also increases. The function is increasing on the interval ([-4,\infty))
• Decreasing: A function is decreasing if, as (x) increases, (y) decreases. There is no interval where the function is decreasing.
• Constant: A function is constant if, as (x) increases, (y) remains the same. There is no interval where the function is constant.

Relative Maximum and Minimum

• Relative Maximum: A relative maximum is a point where the function changes from increasing to decreasing. Since the function is always increasing, there is no relative maximum.
• Relative Minimum: A relative minimum is a point where the function changes from decreasing to increasing. The function has a relative minimum at the point ((-4,1))

Answer:

• Domain: ([-4,\infty))
• Range: ([1,\infty))
• (x) - intercept: None
• (y) - intercept: Approximately (2.5)
• Increasing Interval: ([-4,\infty))
• Decreasing Interval: None
• Constant Interval: None
• Relative Maximum: None
• Relative Minimum: ((-4,1))