The function $f(x) = e^x$ is transformed by a vertical dilation of factor $a$, where $a > 0$, followed by a reflection in the $x$-axis, and then a translation of $b$ units upwards, where $b$ is a real number. The resulting function is $g(x)$.
Explain how the values of $a$ and $b$ affect the existence, location, and equation of any horizontal asymptotes of the transformed function $g(x)$.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 4 marks, testing your understanding of Original vs. Transformed Function Graphs. It falls under Functions, relations and graphs in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers transformations, polynomial functions, power functions, exponential functions, logarithmic functions, circular functions, and combinations of these.
the relation between the graph of an original function and the graph of a corresponding transformed function (including families of transformed functions for a single transformation parameter)
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