2.3 Getting Information from the Graph of a Function
Ideas in this lesson
Read graph values, level sets, and net change
Read domains and ranges with holes and endpoints
Compare graphs and locate intersections
Solve equations and inequalities graphically
Identify increasing, decreasing, and constant intervals
Combine formula and graph information
Distinguish local extrema, coordinates, and global bounds
Approximate polynomial turning points using technology
Analyze radical and rational extrema on their domains
Interpret graphical stories in context
Use graphs to compare and optimize physical models
Construct monotone signed functions and discuss optimization
Prove order-preserving transformations and minimize distance
Read graph values, level sets, and net change · Worked example
Using the complete graph, solve f(x)≥4.
Answer: \(\{-3\}\cup[0,3]\)
The left endpoint alone meets the level before the middle crossing. The rising segment crosses the level at x=0. From 0 through 3 the graph is on or above the level, including the final endpoint.