Question

(b) what is the y - intercept of the function? (0,?) (c) what are the x - intercepts of the function? (these are also known as the functions zeros because they are where f(x)=0.) (d) would you characterize the function as increasing or decreasing on the domain interval - 5≤x≤ - 1? explain your choice. (e) give one additional interval where the function is increasing. (f) give one additional interval where the function is decreasing.

Explanation:

Step1: Identify y - intercept

The y - intercept is the value of the function when \(x = 0\). Looking at the graph, when \(x=0\), the function value \(y = 4\). So the y - intercept is 4.

Step2: Identify x - intercepts

The x - intercepts are the values of \(x\) for which \(y=f(x)=0\). From the graph, the x - intercepts are the x - values where the graph crosses the x - axis. They are the points where the function's value is zero.

Step3: Analyze increasing and decreasing intervals

To determine where the function is increasing or decreasing in the interval \(-5\leq x\leq - 17\), we look at the slope of the graph. If the slope is positive, the function is increasing; if negative, it is decreasing. Since \(-5>-17\), there is a mistake in the interval \(-5\leq x\leq - 17\). Assuming you might mean \(-17\leq x\leq - 5\), we observe the graph in that range.

Step4: Find additional intervals

To find an additional interval where the function is increasing or decreasing, we look at other parts of the graph not already considered.

Answer:

(b) The y - intercept of the function \(y = f(x)\) is 4.
(c) The x - intercepts of the function are the x - values where \(f(x)=0\) (points where the graph crosses the x - axis).
(d) There is an error in the interval \(-5\leq x\leq - 17\) as written. Assuming it's \(-17\leq x\leq - 5\), we would analyze the slope of the graph in that range to determine if it's increasing or decreasing.
(e) An additional interval where the function is decreasing could be, for example, looking at the part of the graph where it is going down - say from the local maximum to the next local minimum (the exact interval can be determined by reading the x - values from the graph). An additional interval where the function is increasing could be from a local minimum to a local maximum (again, read the x - values from the graph).
(f) An additional interval where the function is decreasing: Suppose from \(x = a\) to \(x = b\) (read \(a\) and \(b\) from the graph where the graph is sloping downwards).