Describing Function Behavior In Exercises 41–48,use a graphing utility to graph the function and visuallydetermine the open intervals on which the function isincreasing, decreasing, or constant. Use a table of valuesto verify your results.41. f(x) = 3 42. g(x) = x43. g(x) = 12 x2 − 3 44. f(x) = 3x4 − 6x245. f(x) = √1 − x 46. f(x) = x√x + 347. f(x) = x32 48. f(x) = x23

Q: In Exercises 43 and 44, graph the functions. Notice in each case that the numerator and denominator…

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Q: 2. Find traits and sketch the graph the equation for a function g (æ) that reflects the function f…

A: Note that, to reflect a function fx over the x axis, find -fx. Here, the given function is…

Q: 2) Using the graphing process, Graph the function f (x) = r+3 X-1

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Q: snip

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: B A f(x) = 4(1.25)* ef(x) = 2(0.9) ef(x) = 2(1.62) e f(x) = 2(1.25)* ef(x) = 2(0.69)* Of(x) =…

A: Consider the figure

Q: In Exercises 49 and 50, (a) draw the graph of the function. Then find its (b) domain and (c) range.…

A: we have to (a)draw the graph of the functions: 49) fx=-3-x+2 50) fx=2x+4-3 then we have to find: (b)…

Q: 15) In Exercises 91–94, use the graphs of f and g to evaluate each composite function. 4 3+ 2 y =…

A: (fog)(x) = f[g(x)]

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.