A college has a financial aid formula that applies to applicants whose family's income is below a certain threshold. The financial aid can be determined by the function f(x)=25000+3000x,f(x)=25000+3000x, where xx is the number of siblings (including half siblings and step siblings) that the applicant has living in their household. Find and interpret the given function values and determine an appropriate domain for the function

Q: The maximum value of f(x) is 1+4x+x2

A:

Q: Find the domain of the function h(x) = √(x - 3) + √(x + 4)

A:

Q: Find the domain of the function. h(x) = √(3x - 1)

A: We have to find the domain of the function: hx=3x-1 We know for any square root function y=fx, fx≥0…

Q: Find the points on the graph for the function at the value f(x) = 3. x2 7x + 12

A:

Q: The total revenue for Dante's Villas is given as the function R(x)=500x−0.5x2 , where x is the…

A: Given Rx=500x - 0.5x2

Q: Find the maximum or minimum value of the function. f(x) = 2x2 + 4x - 1

A: We know, for a quadratic equation of the form ax2+bx+c=0,a>0 the minimum value is obtained at…

Q: f(x)= 2x² – 8x- 3 on the given interval [1,3].

A: Given f(x)=2x2-8x-3 on [1,3]

Q: Select the graph of the function. 2x +1 x<0 f(x)= 1-x x20

A:

Q: Find the maximum or minimum value of the function. f(x) = 3 - 4x - x2

A: f(x) = 3 - 4x - x2

Q: Find the domain and range of the function. f(x) = 1/x2

A:

Q: Let f(x) = 2x - 5. g(x) = 4x - 1, h(x) = x2 + x + 2. Evaluate the function (f ∘ g)(0) without…

A: f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x2 + x + 2   g(0)= 4*0 - 1        = 0 - 1        = - 1 g(0)= - 1

Q: If f(x)=(3m-2)x+6 is a constant function m =?

A: For the constant function the coefficient of x should be zero.

Q: Find the local minimum and maximum values of the function    f (x) =  3x4  -4x3 -12 x 2  +5

A: Given function is fx=3x4-4x3-12x2+5. Compute the derivative. f'x=3x4-4x3-12x2+5'=12x3-12x2-24x…

Q: Find the domain of the function f(x) = √(x - 3)

A:

Q: Consider the function f(x) = 2x° + 9x- 108x + 3, - 6 < x < 4. This function has an absolute minimum…

A: f(x) = 2x3+9x2-108x+3f'(x) = 6x2+18x-108f'(x) = 0 6x2+18x-108=0 x2+3x-18=0(x+6)(x-3)=0x=-6,3 where 3…

Q: The amount of money (in billions of​ dollars) lent to customers with credit scores below 620 for…

A:

Q: Consider the function f(x) = 2x³ + 18x² 162x + 6, - 9 < x < 4. This function has an absolute minimum…

A:

Q: Consider the function f(x) = x* – 98x + 1, - 6 < x < 15. This function has an absolute minimum value…

A:

Q: Find the zeroes of the function  f(x) = x/(x2-1)

A: Answer and explanation is given below...

Q: What is the maximum value of the function f(x) = −x2 + 2x + 4?

A:

Q: Find the maximum or minimum value of the function. g(x) = 100x2 - 1500x

A: Given function is  g(x) = 100x2 - 1500x

Q: Is f(x)=x2 - 11 is an example of a non-linear one to one function? Find its Domain and Range if it…

A: f(x) = x2  - 11 It is quadratic function.

Q: In Problem,find the domain of each function.

A: Given function is: qx=-x-2 We have to find the domain of qx.

Q: Consider the function f(x) = 2x³ + 6x² - 90x+5, -5 ≤ x ≤ 4. This function has an absolute minimum…

A:

Q: Find the range of the function f(x) = x² - 2x - 4.

A:

Q: In Problem,find the domain of each function.

A: Given: P(x)=2x-1 To find the domain  of the function.

Q: The maximum value of the function f(x)= x3-5x-4 occurs at

A: Given function fx=x3-5x-4

Q: If f(x) = ax + b with a + 0, how are the zero of f and the x-coordinate of the x-intercept of the…

A: To find x-intercept of a function f(x), we put f(x)=0. To find zeroes of f(x), we put f(x)=0. i.e.…

Q: Find the intervals on which the function f(x) = x² – 6x + 10 is increasing and decreasing.

A:

Q: Find the intervals on which the function f(x)=x−4x2 is increasing and decreasing.

A: Given function:

Q: the function f(x)=x^3-3x^2+5x has neither maximum nor minimum?

A: Consider the given function. fx=x3-3x2+5x Find the derivative of the function. f'x=3x2-6x+5x Put the…

Q: The weekly revenue (in dollars) earned from selling x porcelain vases is given by the function R(x)=…

A:

Q: f(x)=x3 - 2 is an example of a non-linear one to one function? Find its Domain and Range if it…

A:

Q: Consider the function f(x) = 2x³ + 27x² – 60x + 5, - 10 < x < 2. This function has an absolute…

A:

Q: Find the domain of the function f(x) = V15x -3.

A: Given,            f(x) = 15x - 34

Q: Consider the function f(x)=2x^3+27x^2-60x+1, -10≤x≤2. Find the absolute minimum and maximum value…

A: Answer and explanation is given below..

Q: What is the maximum value of the function f(x) = −x2 + 2x + 4? (Enter an exact number.)

A: Given,

Q: Find the absolute maximum and minimum value of the function  f(x) = x / 49 + x^2

A:

Q: Find all x-intercepts of the function f ( x ) = ( x + 3 ) ( x − 4 ) ( x − 9 ).

A: Since, our aim is to find all x-intercepts of the function given below:-f(x)= (x+3)(x-4)(x-9)   -(i)

Q: The graph of function f(x) = 5x – 7x² – 8 is concave - downward on

A: For the given Function  f(X) is concave downward on (-∞, 7/15)  So none of the options is correct.

Q: Graph the piecewise-defined function. 4. f(x)=2x- 1, if x>1

A: Given function is : fx=x+5  , if x≤12x-1 , if x&gt;1 To draw the graph of given function.

Q: If fx) is a differentiable function such that f(-2)=-1 and g(x)-f(3x+1), then what is g'(-1)?

A: Use chin rule to differentiate g(x).

Q: Let f(x) = 2x - 5. g(x) = 4x - 1, h(x) = x2 + x + 2. Evaluate the function (g ∘ f)(0) without…

A: Consider the function: fx=2x-5,  gx=4x-1,  hx=x2+x+2

Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing.

A: Topic = Functions

Q: Find the maximum or minimum value of the function. f(x) = −x2 + 10x − 14

A: The given function is

Q: Find the slope of the graph of the function f (x) 4(5x + 6)² at x = 3.

A:

Q: What value should be assigned to a to make the function x<3 |(x) = {x²- 1, (x)%3D (2ax, x23…

A: Given:   Function equation is given

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.