Question

unit 1 lesson 4 practice problems 1 use the graphs to answer the questions below. graph a graph b graph c graph d a which graphs are increasing on the interval (-6, -2)? b which graphs are always positive? c which functions are continuous? which are discontinuous? explain how you know. d identify the interval where graph b is decreasing and describe it using interval and inequality notation. e identify the interval where graph b is negative and describe it using interval and inequality notation.

Explanation:

Step1: Analyze increasing - interval for part a

For a graph to be increasing on an interval, as \(x\) values increase in the interval \((-6,-2)\), \(y\) values should also increase. By visually inspecting the graphs, we can determine which ones meet this criterion.

Step2: Analyze positive - value for part b

A graph is always positive if all of its \(y\) - values are greater than 0 for all \(x\) - values in its domain.

Step3: Analyze continuity for part c

A function is continuous if there are no breaks, jumps, or holes in the graph. A discontinuous function has at least one of these features.

Step4: Analyze decreasing - interval for part d

For a graph to be decreasing, as \(x\) increases, \(y\) decreases. We find the interval on Graph B where this occurs and write it in interval and inequality notation.

Step5: Analyze negative - interval for part e

We find the interval on Graph B where \(y<0\) and write it in interval and inequality notation.

Answer:

a. Without seeing the actual graphs clearly, assume we visually inspect them. If a graph has a positive - slope in the interval \((-6,-2)\), it is increasing. For example, if Graph A has a positive - slope in this interval, then Graph A is one of the answers.
b. Again, visually inspecting the graphs, if a graph lies entirely above the \(x\) - axis, it is always positive.
c. Continuous graphs have no breaks. If a graph has a jump or a hole, it is discontinuous. For example, if Graph C has a jump, it is discontinuous.
d. Suppose after inspection, Graph B is decreasing on the interval \((-4,0)\). In interval notation: \((-4,0)\), in inequality notation: \(-4 < x<0\).
e. Suppose after inspection, Graph B is negative on the interval \((-2,2)\). In interval notation: \((-2,2)\), in inequality notation: \(-2 < x<2\).