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.
1d. 1e.
![For questions 1 and 2, consider the function f(x) = ÷x2.
+ x +1 on the interval [0, 4].
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We have to determine whether it is underestimate or overestimate.
We know that, if the graph is concave down(second derivative is negative) then the line will lie above the graph
and the approximation is an overestimate, otherwise it is underestimate.(simply if the graph is concave up).
d) Here from graph we can easily observed that the graph of f(x) = , on [0,4] given above is
concave up on [0,4]. So the area approximation for this graph going to be an overestimate.
e) Now we have to calculate this area approximation.
We know the graph of f(x) given above is increasing on the interval [0,4], then the left sum is an
underestimate of the actual value and the right sum is an overestimate.
Therefore, we need to calculate right sum because our area approximation here for given function is overestimate.
Let us divide given interval [0,4] in 4-equal rectangles.
So length of each rectangle is unit,
So the right end points are
Hence,
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Solved in 3 steps
