Begin by graphing the absolute value function, f(x) = |X|. Then use transformations of this graph to graph the given function. g(x) = - 3 |x- 5|+6 What transformations are needed in order to obtain the graph of g(x) from the graph of f(x)? Select all that apply. O A. Reflection about the x-axis O B. Vertical shift O C. Vertical stretch/shrink O D. Reflection about the y-axis O E. Horizontal stretch/shrink O F. Horizontal shift Choose the correct graph below. O A. O B. OC. D. -10 10 -10 10 -10 -10 10
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.
Consider the function is f(x)=|x|
Then the function g(x) is obtained as,
Shift the graph of f(x) 5 units to the right horizontally.
f(x)=|x-5|
Then, vertically shrink or multiply the function by a factor of 3 as,
f(x)=3|x-5|
Then, reflect the graph along the x axis as,
f(x)=-3|x-5|
Then, shift the graph 6 unit vertically upward.
f(x)=3|x-5|+6
Thus, the options that apply are A, B, C, and F.
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