Let f(x) = r - 4, g(x) = x² + 4, and h(r) = 1 + 5. Without a calculator, match the functions in (a)-(f) to the descriptions in (i)-(viii). Some of the functions may match none of the descriptions. f(x) 9(r) g(x) f(z) g(x) h(x) h(x) (a) (b) (c) y- F(x) h(r*) (f) y (d) y = (e) y = h(x) (g) y = g(x) (h) y = f(r) g(x) (i) Horizontal asymptote at y = 0 and one zero at z = -5. (ii) No horizontal asymptote, no zeros, and a vertical asymptote at z = -5. (iii) Zeros at z = -5, r= -2, and z = 2. (iv) No zeros, a horizontal asymptote at y = 0, and a vertical asymptote at z= -5. (v) Two zeros, no vertical asymptotes, and a horizontal asymptote at y = 1. (vi) No zeros, no vertical asymptotes, and a horizontal asymptote at y = 1. vii) Horizontal asymptote at y = -4. viii) No horizontal asymptotes, two zeros, and a vertical asymptote at z = -5.

Q: Let f(x)=9x+8‾‾‾‾‾‾√f(x)=9x+8 and g(x)=x+9g(x)=x+9 be functions from ℝR to ℝR. Find the following.…

A: We will find out the required values.

Q: Given the following function:  f(x)=(x−1)3(x+2)f(x)=(x−1)3(x+2).  What happens at the zero of x=1x=1

A: We have given function fx=x-13x+2.

Q: (3) (3) 5. Simplify f(x) = 3 + i (a) f(x) = g(x) and g(x) = -5 +i (b) F(x) • 9 (X) (3+1)(-5+1)

A:

Q: For problem 1-2, use f (x) = x² + 1 and g(x) = Vx – 1 to determine the indicated function. State the…

A:

Q: The function f ( x) = (x-1)2-3 is not one-to-one. True O False

A: A function f is one-to-one if every element of the range of f corresponds to exactly one element of…

Q: Given two functions f(x) = x² – 3x and g(x) : - = x + 13, find the following. a) f( – 2) + g( – 2)…

A:

Q: The functions f, g and h are defined for xeR by f(x) = x², g(x) = 2x and h(x) =x+ 2. Find each of…

A: The terms are:-

Q: If f(x) = x3 + 1, then give the following

A: Consider the function: fx=x3+1

Q: (a) f(x) =; 2x+1 x²+x-2 (b) g(x) x²+1 (c) h(x) = v4 – x + vx² – 1 %3D

A: The given functions are a.) fx=2x+1x2+x-2 b.) gx=x3x2+1c.) hx=4-x+x2-1 Domain of a function is the…

Q: Let f(x) = x´ + 6x and g(x) = 5 – x. H() =D (Simplify your answer.)

A:

Q: (a) ( (b)( (c) ( (d) ( ) satisfies g(x). ) satisfies g(x). ) satisfies g(-3x). ) satisfies -g(3x).

A:

Q: If f(x) = x' + 2x (a) fog I and g(x) 2x 3, find each of the following functions (b) g f (c) g g-9

A:

Q: Suppose f(x) = – x + 1. Compute each of the following.

A: Given,           fx=-x+1

Q: If f(x) = x + 6 and g(x) = x² - 5, find the following. b. g(f(0)) d. g(f(x)) a. f(g(0)) c. f(g(x))

A: We are authorized to answer three subparts at a time since you have not mentioned which part you are…

Q: (3) (3) 5. Simplify f(x) = 3 + i (a) f(x) - g(x) and g(x) = -5 +i (b) f(x) • g(x)

A: Given Function are as follows

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.