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.
In Problems 14-17, refer to the following graph of y = f(x)
The notation implies the limit calculated by approaching the point from the right. The notation implies the limit calculated by approaching the point from the left.
If for a function the it has the horizontal asymptote . If the function tends to as then the function has a vertical asymptote .
From the graph it is clear that function has horizontal asymptote and has a vertical asymptote .
14.
Limit to be calculated is . From the graph we see that as the function approaches the line .
Hence, .
15.
Limit to be calculated is . From the graph we see that as the function approaches the line .
Hence, .
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