b. Suppose the function f determines the volume of the box (in cubic inches) given a cutout length (in inches). Write a function formula for f. f(x) = x(5-2x)(7-2x) Preview c. What is the domain of f? Enter your answer as an interval. Hint. |(-00,00) Preview

Q: 0. 5.

A: **If graph of function is symmetric about the origin is called odd function . **If graph of function…

Q: Determine if this function is even, odd or neither. Justify the answer. F(×)=3X2+×-5

A:

Q: Use the horizontal line test to determine whether the function is one-to-one. y = /x -3 Is the…

A: Consider the graph

Q: Use the vertical line test to determine if the relation shown in the graph below is a function. o…

A: To use the vertical line test, to check whether the given graph is a function or not.

Q: Find the interval where the function, - + 25 is decreasing? None (-00,-0.9375) • (-00, 0.9375)…

A: Given,  Then function  25x2-34x+25  We have to find the intervals in which it is decreasing.

Q: 5 Write the algebraic representation for the following piecewise function, using function notation.…

A:

Q: Find the inflection point of the following function. (x) = 3x³ - 3x² + x + 1 %3D 3,0) -3,0) 1/3,0)…

A:

Q: Write the function g(x) (in blue) in terms of the function f(x) (in red). 2 -3 -2 6. -1 5.

A:

Q: a. Write a function f that determines the circumference of a circle in cm, C, in terms of the radius…

A: To find:- a. Write a function f that determines the circumference of a circle in cm, C, in terms of…

Q: Use function notation to Express the weight of pig in pounds as afunction of it's age in days d.

A: Given: Weight of pig in pounds is function of its age in 'd' days

Q: -5 0. 10 -2 5. 2.

A:

Q: 減ャ2

A: Domain of f(x) means set of value of x for which f(x) is defined.

Q: a) find the domain and range of the function в Сху) =5 4-x2_ye 4-х

A:

Q: A function is shown in the table below. If included in the table, which ordered pair, (-4,1) or…

A: To find which ordered pair makes  the given function a relation.

Q: Which of the following tables does not represent a function?

A: we know that for a function at each value of x, it gives only one value of y here, for option B at…

Q: (c) If b = 1, what is the range of this function? (Enter your answer using interval notation.)

A: Topic = Function

Q: Use the vertical line test to determine if the relation shown in the graph below is a function. 5-…

A:

Q: 5-4-3 2-1 10 9 8 7 6 5 1 y 4 32 3+ 2+ 1 2 234 3 4 5 -6 1 2 3 4 5 X

A: Please see the below picture for detailed solution.

Q: The graph shows the relationship between the time, in seconds, and the distance traveled by a…

A: This graph is only shown in positive X, y plane Domain of a function is all the values of x where…

Q: Refer to the graph ofthe function and complete the statements 44) Asx -o0, f(x)- As x → n,f(x)→ 44)…

A: In the given graph, there are vertical asymptotes and horizontal asymptotes.Clearly, left hand limit…

Q: Write an equation for the function that includes the points. X F(x) -4 0.53 -3 5.3 -2 53 -1 530

A:

Q: B. Use the vertical line test to determine whether the graph is a function. Write yes or no on the…

A:

Q: Refer to the function: f(x) =[x] determine f(-8.8)

A: Explanation of the answer is as follows

Q: (ii) f (æ) =| -a²+ 2æ³, -æ² – 2a®, -1 <æ<0 -x? + 2x³, 0 < x <1

A: Given function is fx=−x2−2x3,   −1≤x≤0−x2+2x3,      0≤x≤1 To determine whether the above function is…

Q: Which statement is true about function f, which is shown in the graph? f(x) = -875 + 4x3 + 5x

A:

Q: Find the domain of the following function. Write your answer in interval notation.

A: Domain means the possible values of x. All real numbers are possible for the value of x. So the…

Q: What is the vertex of the function f(x) = (x- 1)2- 5? O (-1, -5) O (1, -5) O (-5, 1)

A: Given:          f(x) = (x-1)2-5 Let               y = f(x)Then               y =  (x-1)2-5→If you…

Q: Write a function formula for f.

A: A sinusoidal function can be expressed in the form of sine and cosine function as, y=AcosBx-C+D or,…

Q: Write the domain of the following function using interval notation. 3x-5 f(x) 4-3x

A:

Q: Describe the domain and range of this function. f (x) = 2(3)"-1 + 4 10 8. 5- -3 9.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: a. Write a function f that determines the circumference of a circle in cm, C, in terms of the radius…

A: We have to find f(g(24)) g(f(24)) and f(g(134.5))

Q: a general, the zeros of a function

A: Zero of a function :

Q: The plot below represents the function f(x) 5 -3-2 -2- Evaluate f(-3) f(- 3) = %3D Question Help:…

A: To find  f(-3) from given graph  Method :- we use inspection method

Q: Give the domain and range for the function shown below. Use interval notation. 10+ 7 4 10 -9 -8 -7…

A:

Q: Determine the domain of the following function in interval notation: A -3, o0) B -3, 0) C ( -3, 00)…

A:

Q: Make a table of values that shows the function values for f(x) = 17 - x and g(x) = 48 - 2* for x =…

A: We have functions fx=17-x3  and gx=48-2x We need to evaluate the values of f(x) and g(x) at…

Q: Which of the following relations is a function? -2 a. 4 -6 -2 0. -2 d. A

A:

Q: Utilize the function to evaluate the indicated expressions. Simplify. f(x) = 6x-18; ƒ (-), f(x)

A:

Q: Use the graph of the function f shown to determine f(10). (10, 8) (-6, 6) (-3, 4) (0, 2) (-11, 2)…

A: From the graph of the given function:                               We need to determine:…

Q: Children in Preschool and Kindergarten :: Based on data provide by the Census Bureau, the number of…

A:

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

A: fx=-x+1,-10≤x&lt;-3x2-9,-3≤x≤32x+1,3&lt;x&lt;5 we have to find the positive region, negative region…

Q: The number of public elementary and secondary school teachers (in millions) in a particular year can…

A: Solution: f(x)=2.638 + 0.183ln x

Q: Use the graph of the function to find the domain and range of f. (Enter your answer using interval…

A: By seeing the graph  domain of function is [-1,3] Range of function is (-infinity,7]

Q: 5 4 3 -5 -4 -3 -2 1 2 3 4 5 -1 -1 -2 4 -5 LO 2. 3. LO

A:

Q: State the open intervals over which the function is (a) increasing, (b) decreasing, and (c)…

A: We can find the required intervals as below.

Q: -4 -2 -10 -8 -4 -2 4. 6 8, 10 -2 -8 -10 for f(x) = for

A: Write the equation of two straight lines separately and than define the domain.

Q: 4 21 -4 -2 0. 2. 4 -2

A: We are given the graph of a function and we are required to find whether the function is even, odd…

Q: Determine if the function is even, odd or neither f(x) = x4 - x2 + 2

A: We plug -x in place of x and find f(-x) and simplify.

Q: The plot below represents the function f(x) 5- -5 -4 -3 -2 -2 -3- -4- -5+ Evaluate f(1) f(1) =…

A: The aim is to evaluate f(1) x=1 is to the right of the vertical axis. Move in the direction of the…

Q: 4) Use the given graph of a function f to determine when the function is increasing, decreasing, or…

A: Function is increasing when slope of tangent is positive and decreasing when slope of tangent line…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.