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.
Let g(x) be given as attached, where f is the function whose graph is shown in the figure. (a) Estimate g(0), g(2), g(4), g(6), and g(8). (b) Find the largest open interval on which g is increasing. Find the largest open interval on which g is decreasing. (c) Identify any extrema of g. (d) Sketch a rough graph of g
Solution:
Consider the given function g(x) =
On the observation of graph of f(t),
(a) Now, g(0) = 0, g(2) = 2f(2) = 2 x (-4) = -8, g(4) = 4f(4) = 4 x (0) = 0
g(6) = 6f(6) = 6 x (4) = 24
g(8) = 8 f(8) = 8 x 0 = 0
(b)
Calculate g(1) = 1.f(1) = 1.(-2) = -2
g(3) = 3f(3) = 3 x (-2) = -6
g(5) = 5f(5) = 5 x (4) = 20
g(7) = 7f(7) = 7 x (4) = 28
The largest open interval of g(x) in which g(x) increasing is (2, 7)
The largest open interval of g(x) in which g(x) decreasing is
Step by step
Solved in 2 steps with 1 images
