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YES!
Simply by taking a quick glance at a graph, you can see several characteristics of the function: local minimums/maximums, points of inflection, end behavior, asymptotes, etc etc...
If you wanted to find these without the graph, you would have to do some math which might end up being very time consuming for very complicated functions. Even worse: what if the function is not elementary, and you can't express it in terms of finite arithmetic operations?
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Find the amplitude and period of the functions and sketch their graphs y equals sin -x?
y = sin(-x)Amplitude = 1Period = 2 pi
What is vertical stretch and horizontal stretch?
They are transformations of plane graphs.
What are graphs that cannot represent functions?
Consider the graph of y= +/- sqrt(x). Notice that, for any value of x greater than 0, there are two values of this relation. To be a function a relation has to assign one value in the range to each value in the domain. So this cannot be a function, yet it has a perfectly ordinary graph.
Do all functions have integrals?
No, all functions are not Riemann integrable
What do the peaks on the graphs in figure 7 3 represent?
The peaks are called the activation energy. It is the energy used to get the reaction going.
