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 - graphs on (-6,-2)

Check each graph for upward - trend in the interval (-6,-2). Graph A is decreasing in this interval. Graph B is increasing in part of this interval. Graph C is constant. Graph D is increasing in the interval (-6,-2). So Graph B and Graph D are increasing on (-6,-2).

Step2: Determine always - positive graphs

Check if the y - values of the graphs are always above the x - axis. None of the given graphs are always positive as all of them cross or go below the x - axis at some points.

Step3: Identify continuous and discontinuous functions

A continuous function has no breaks, jumps, or holes. Graph A is continuous as it has no breaks. Graph B is continuous as it has a smooth curve without breaks. Graph C is discontinuous because of the jumps in the graph. Graph D is continuous as it has no breaks or jumps.

Step4: Find decreasing interval of graph B

Observe the part of graph B where it is going downwards. Graph B is decreasing on the interval (-4, - 2). In inequality notation: -4 < x < -2.

Step5: Find negative interval of graph B

Find where the y - values of graph B are below the x - axis. Graph B is negative on the interval (-6,-4). In inequality notation: -6 < x < -4.

Answer:

a. Graph B, Graph D
b. None
c. Continuous: Graph A, Graph B, Graph D; Discontinuous: Graph C. Reason: Continuous functions have no breaks, jumps, or holes; Graph C has jumps.
d. Interval notation: (-4,-2); Inequality notation: -4 < x < -2
e. Interval notation: (-6,-4); Inequality notation: -6 < x < -4