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.
Use the graph of y = f(x) to graph the function. g(x) = f(2x)
given:
the graph of the function y=f(x).
we have to graph the function g(x)=f(2x).
as we know that if we have a function h(x) having period 'c' then the function y=h(ax) has a period of .
but the amplitude of both the functions y=h(x) and y=h(ax) will remain same.
that is both have difference in their periods only but the amplitude will remain same.
so only the frequency changes but the amplitude remains the same.
that implies as the frequency changes therefore, the graph will either stretch or contract horizontally depending upon whether the period has increased or decreased but as there is no change in amplitude there will be no vertically stretching or contraction.
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