the graphs of the functions g and h are shown below. for each graph, find the absolute maximum and absolute…
the graphs of the functions g and h are shown below. for each graph, find the absolute maximum and absolute minimum. if no such value exists, click on \none\. assume that the dashed line shown is a vertical asymptote that the graph does not cross. (a) graph of g (b) graph of h absolute maximum of g: absolute minimum of g: absolute maximum of h: absolute minimum of h:
Answer
Explanation:
Step1: Analyze graph of g
For the function (g), we look at the highest and lowest (y -)values. The highest (y -)value occurs at the left - hand endpoint. The lowest (y -)value occurs at the right - hand side near the vertical asymptote.
Step2: Determine absolute maximum of g
The absolute maximum of (g) is the (y -)coordinate of the left - hand endpoint. From the graph of (g), the absolute maximum of (g) is (5).
Step3: Determine absolute minimum of g
As (x) approaches the vertical asymptote from the left, the function (g(x)) decreases without bound. So, the absolute minimum of (g) does not exist. We write "None".
Step4: Analyze graph of h
For the function (h), we find the highest and lowest (y -)values on the entire graph.
Step5: Determine absolute maximum of h
The absolute maximum of (h) is the (y -)coordinate of the highest point on the graph of (h). From the graph of (h), the absolute maximum of (h) is (3).
Step6: Determine absolute minimum of h
The absolute minimum of (h) is the (y -)coordinate of the lowest point on the graph of (h). From the graph of (h), the absolute minimum of (h) is (- 3).
Answer:
Absolute maximum of (g): (5) Absolute minimum of (g): None Absolute maximum of (h): (3) Absolute minimum of (h): (-3)