Draw a possible graph of y = f(x) given the following information: Do this on a separate sheet of paper. f ′ (x) > 0 for 3 < x < 6 f ′ (x) < 0 for x < 3 f ′ (x) < 0 for x > 6 f ′ (x) = 0 for x = 3 and x = 6 a. the graph is decreasing on (−∞, 3), increasing on (3, 6) and decreasing from (6, ∞) b. the graph is increasing on (−∞, 3), decreasing on (3, 6) and increasing from (6, ∞) c. the graph is decreasing on (−∞, 3), increasing on (3, 6) and constant on (6, ∞) d. The graph is decreasing on (−∞, 3), has slope at x = 3 zero and has slope at x = 6 greater than zero, but decreasing from (6, ∞): The function could be decreasing or increasing on (3, 6). e. None of these
Transformation of Graphs
The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.
Exponential Functions
The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.
Draw a possible graph of y = f(x) given the following information:
Do this on a separate sheet of paper.
f ′ (x) > 0 for 3 < x < 6
f ′ (x) < 0 for x < 3
f ′ (x) < 0 for x > 6
f ′ (x) = 0 for x = 3 and x = 6
| a. |
the graph is decreasing on (−∞, 3), increasing on (3, 6) and decreasing from (6, ∞) |
|
| b. |
the graph is increasing on (−∞, 3), decreasing on (3, 6) and increasing from (6, ∞) |
|
| c. |
the graph is decreasing on (−∞, 3), increasing on (3, 6) and constant on (6, ∞) |
|
| d. |
The graph is decreasing on (−∞, 3), has slope at x = 3 zero and has slope at x = 6 greater than zero, but decreasing from (6, ∞): The function could be decreasing or increasing on (3, 6). |
|
| e. |
None of these |
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
