using the given graph of the function f, find the following. (a) the intercepts, if any (b) its domain and…
using the given graph of the function f, find the following. (a) the intercepts, if any (b) its domain and range (c) the intervals on which it is increasing, decreasing, or constant (d) whether it is even, odd, or neither on which interval(s) is the graph constant? select the correct choice below and fill in any answer boxes within your choice. a. the graph is constant on . (type your answer in interval notation. use a comma to separate answers as needed.) b. the graph is not constant on any interval.
Answer
Explanation:
Step1: Analyze the graph for intercepts
The x - intercepts are the x - values where y = 0. From the graph, the x - intercepts are x=-3, x = - 1, x = 1, x = 3. The y - intercept is the y - value where x = 0, and y=-1.
Step2: Determine the domain and range
The domain is the set of all x - values for which the function is defined. From the graph, the domain is [-4,4]. The range is the set of all y - values. The range is [-1,1].
Step3: Identify increasing, decreasing and constant intervals
The function is increasing where the graph goes up as we move from left to right. It is increasing on (-3,-1) and (1,3). It is decreasing on (-4,-3), (-1,1) and (3,4). It is not constant on any interval.
Step4: Check for even or odd function
A function is even if f(x)=f(-x) (symmetric about y - axis) and odd if f(-x)=-f(x) (symmetric about origin). The graph is not symmetric about the y - axis or the origin, so it is neither even nor odd.
Answer:
(a) x - intercepts: x=-3,-1,1,3; y - intercept: y = - 1 (b) Domain: [-4,4]; Range: [-1,1] (c) Increasing: (-3,-1),(1,3); Decreasing: (-4,-3),(-1,1),(3,4); Constant: None (d) Neither