Suppose that the function f is defined for all real numbers as follows. x²+1 if x<1 f(x) = 2 if x=1 8-3x if x>1 Graph the function f. Then determine whether or not the function is continuous. 12- 10+ 8+ 6- Is the functionf con 2- -12 -10 8. -6 6. 10 12. +2- -4+ -6- -8+ -10- -12- Explanation Check

Q: Use the graphs to evaluate the expressions below. 6 4 N 1 f 5 4 f(x) g(x) f(g(3)) = = g(ƒ(1)) =…

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Q: 1) Give an example of a function whose domain does not include x = -2 or x = 2.

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Q: Suppose that the function fis defined, for all real numbers, as follows. f(x) = x-3 if x -2 Graph…

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Q: for all real nombers, as fllou) -7

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Q: ーx+ 1, - 10 sx<-3 x - 9, - 3 <x< 3 2x + 1, 3 <x < 5 f (x) =

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Q: Graph the function f(x)=2x-1₁ for -4 ≤ x ≤ 4 where x is a real number

A: The ceiling function is a function that gives a value to the closest integer greater than or equal…

Q: 16 (+4,12) 12 -6 -4 -2. 2. 4. -12 (4,-12). 16 Ise interval notation. This function has domain and…

A: Domain is defined as the set of values of x for which the function is defined. While range is the…

Q: If(5, –2) is in the function f (x), then which of the following points will be in the function f'…

A: Given that (5, -2) is in the function f(x). So, we have f(5) = -2 and hence f-1(-2) = 5. Thus, we…

Q: A function f(x) is given by the following set of ordered pairs: {(2,6), (4, 12), (5, 15), (9, 27)}.…

A: The function is represented by the ordered pairs 2, 6, 4, 12, 5, 15, 9, 27. (a) Express fx using…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.