Basic Math question and answers for October 28, 2024
- Q A real estate company balances the books for its business on the first day of each month. It hopes to sell houses every other day of the month. The average...
- Q The function f(x) = 1/4(x - 2) + 10 , x ? 2 is one-to-one-(a) Find the inverse of f and check the answer.(b) Find the domain and the range...
- Q The functions r and s are defined as follows.r(x) = -x+2s(x) = 5x+1Find the value of s (r (-4)).
- Q For f(x) =2/x-5 and g(x)=9/x find the following composite functions and state the domain of each.(a) fog(b) gof(c) fof(d) gog
- Q f(x)=?x +9. Find (x) f-and its domain.A. f-(x) = (x - 9); x?9B. f-(x) = x - 9; x? 9C. f-(x) = (x - 9); x? 0D. f-(x)=x-9;x?0
- Q Consider the following function.Correctv(x) = (x + 7)Step 2 of 2: Determine the domain and range of the original function. Express your answer in interval notation
- Q For f(x) = 6x + 7 and g(x)=x, find the following composite functions and state the domain of each.(a) fog(b) gof(c) fof(d) gog(a) (fog)(x) = 6x +7 (Simplify your answer.)Select...
- Q Solve the problem.The rational functionC(x) =140x100-x'describes the cost, C, in millions of dollars, to inoculate x% of thepopulation against a particular strain of the flu. Determine thedifference in cost between...
- Q Consider the following relation.S = {(8, 7), (1, 9), (5. 5), (9. ?4)}Step 2 of 2: Find the domain and range of the inverse. Express your answer as a set...
- Q Watch the video that describes evaluating combinations of functions.Click here to watch the video.Let f(x)=x-3 and g(x)=x-x. Find and simplify the expression.(f+g)(-2)(f+g)(-2)=(Simplify your answer.)
- Q The functions r and s are defined as follows.r(x)=2x+2s(x)=?2x-2Find the value of s (r(-4)).
- Q Graph of the function f(x) = logi (x). You can only graph integer points, for example you cannot plot the point -1. 1/4) There is one point that can be...
- Q Graph the function. g(x)=-3x Plot five points on the graph of the function: one point with x=0, two points with negative x-values, and two points with positive x-values. Then tap...
- Q The functions q and r are defined as follows.q (x) = -xr(x) = -x+2Find the value of r (q (5)).
- Q The equation, d(t) = 255t + 5654 represents the tuition, d dollars, ata college for the year that is t years since 2002.Find an inverse function for this model.0000-2555654+5654255-5654255+2555654
- Q Find (f g)(1) for the following functions.AnswerHow to enter your answer (opens in new window)f(-2) = -13 and g(1) = -2(fog)(1) =
- Q Determine if the following function is even, odd, or neither.m=|x|/2=1
- Q Consider the following functions.f(x) = -4x and g(x) = x ? 3Find the formula for (f + g)(x) and simplify your answer. Then find the domain for (f + g)(x)....
- Q The functions s and t are defined as follows.s(x)=2x+1t(x)=-2x-2Find the value of s (t (2)).
- Q For f(x) =x/x-7 and g(x) = -6/x, find the following composite functions and state the domain of each.O A. The domain of fog is {x(Type an inequality. Use integers or...
- Q Consider the following functions.f(x) = x + 3 and g(x) = x^1/2Find the formula for (f/g) (x) and simplify your answer. Find domain for (f/g) (x).
- Q The total world population is forecast to beP(t) = 0.00078+ -0.0715t +0.89t + 6.04 (0 ?ts 10)in time t, where t is measured in decades, with t= 0 corresponding to...
- Q The rat population in a major metropolitan city is given by the formula n(t): 58e 0.015t where t is measured in years since 2002 and n(t) is measured in millions.What...
- Q A sample of bacteria is decaying according to a half-life model. If the sample begins with 500 bacteria, and after 10 minutes there are 250 bacteria, after how many minutes...
- Q Expand the function f(x) = -4 (x+5) (x - 2) (x-7)
- Q The function f(x) is given by the set of ordered pairs.{[(8, -3), (0, 4), (1, -5), (2, -1), (-6, 10)}Which is true regarding the function?f(-3) = 8f(3) = 5f(8) =...
- Q Given f(x)= 14/x+5 and g(x)=3?x, find the following expressions.(a) (fog)(4) (b) (gof)(2) (c) (fof)(1) (d) (gog)(0)(a) (fog)(4) =
- Q Write the point-slope form of the equation of the line satisfying each of the following conditions. Then use the point-slope form to write the slope-intercept form of the equation in...
- Q What is the range of the given function?{(-2, 0), (-4, -3), (2, ?9), (0, 5), (-5, 7)}{x|x = -5, -4, -2, 0, 2}{y|y = -9,-3, 0, 5, 7}{x|x = -9,...
- Q For the polynomial below, 2 is a zero.3g(x) = x + 3x - 4x - 12Express g (x) as a product of linear factors.g(x) =
- Q Consider the function f(x) = cos(?/4 x)(a) Find the linearization of f(x) at the point x = 1L(x) =(b) Use the linearization in (a) to estimate the value of cos...
- Q Dan is driving on the highway. He begins the trip with 16 gallons of gas in his car. The car uses up one gallon of gas every 25 miles.Let G...
- Q A piecewise function f (x) is defined by f (x) =3x-1- 4 for x?3(-x + 3x + 4) / (x -7x+12) for x>3Part A: Graph the piecewise function f (x)...
- Q The function f(x)=X+6x-3a. Find an equation for f(x), the inverse function.b. Verify that your equation is correct by showing that f(f(x)) = x and f(f(x)) = x.A. f(x) =a. Select...
- Q Suppose that the relation T is defined as follows.T={(?4, 1), (8, 1), (?8, ?4)}Give the domain and range of T.Write your answers using set notation.
- Q An ice cube is freezing in such a way that the side length s, in inches, is s(t)=-)=t+2, where t is in hours. The surface area of the ice cube...
- Q The half-life of radium-226 is 1,590 years.(a) A sample of radium-226 has a mass of 50 mg. Find a formula for the mass of the sample that remains after t...
- Q If the function y = e-5 is vertically compressed by a factor of 6, reflected across the y-axis, and then shifted up 1 units,what is the resulting function? Write your...
- Q A population of bacteria is initially 500. After two hours the population is 250.If this rate of decay continues, find the exponential function that represents the size of the bacteria...
- Q (1 point) Use the graph of y = (6 - x) / (6 + x) to determine where the function is not differentiable.The function is not differentiable at x =(If...
- Q Turner is baking apple tartlets for a special celebration. He has already made 6 tartlets, andhe can make 3 more tartlets with each additional egg he has in the fridge.Write...
- Q Suppose that the relation H is defined as follows.H={(m, 0), (1, 1), (7, m), (5, n)} Give the domain and range of H.Write your answers using set notation.
- Q The function that converts pounds of Country A to dollars of Country B is f(x) = 1.9738x, where x is the number of pounds of Country A and f(x) is...
- Q Find the linear function with the following properties.f(-4)= 10f(-9) = 11
- Q Find the range of the function f(x) = x - 5x for the domain (2, 4, 7). CRange:
- Q Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list of equations.)5x + 7xA-1vertical asymptote(s) ||r(x) =horizontal...
- Q Let f(x) = 4?If g(x) is the graph of f(x) shifted up 2 units and right 2 units, write a formula for g(x)g(x)=Enter ?? as sqrt(x)
- Q What is a possible equation for this transformed cos function?Select one:a. f(x) = cos(2x) - 3b. f(x) = cos(x-2)-3c. f(x) = 2cos(x) - 3d. f(x) = cos(2x - ?) -...
- Q When performing operations on functions, the domain of the new function after the operation has been performed must include and excludeall prime numbersany negative valuesif it is a quotient function,...
- Q Given f(x) = 1/ x+1 and g(x) = x 4, if you were asked to find ()(x), what would be the restrictions on the domain of the quotient function?Select one:a....
- Q Use implicit differentiation to find an equation of the tangent line to the curve at the given point.y sin (12x) = x cos(2y),(?/2, ?/4)
- Q Consider the function represented by the equation 6q = 3s - 9. Write the equation in function notation, where q is the independent variable.
- Q Which of the following illustrates how the graphs of y = bx and y = (1/b)x with b > 1 are related?A. One is a reflection over the x-axis of...
- Q A country's population in 1990 was 123 million. In 2002 it was 128 million. Estimate the population in 2013 using the exponential growth formula. Round your answer to the nearest...
- Q Find the horizontal asymptote, if it exists, of the rational functiong(x)= (9-x)(3+4x) / (9x^2 +1)
- Q Let g be a function. Which statements are true for all functions g?Select all that apply.For an element x in the range, g(x) represents an element in the domain.The function...
- Q The points at which a graph changes direction (from increasing to decreasing or decreasing to increasing) are calledend points.turning points.minimum points.maximum points.changing points.
- Q On the day a certain celebrity proposes marriage, 8 people know about it. Each day afterward, the number of people who know grows by 50%.Which expression gives the number of...
- Q A 14 gram sample of a substance that's used to preserve fruit and vegetables has a k-value of 0.1095.N = Noe^-ktN0= initial mass (at time t = 0)N = mass...
- Q Find all solutions of the following polynomial equation.21-7x+x-3x = 0
- Q Lexington High School has an annual growth rate of 4.7%. Three years ago there were 1500 students at the school.a. How many students are there now?b. How many students were...
- Q Find equations for the vertical asymptotes, if any, for the following rational function.f(x) =-4x + 16/-2x+7
- Q For the following function, find (a) the critical numbers, (b) the open intervals where the function is increasing, and (c) the open intervals where it is decreasing.f(x) = x^4 +...
- Q Consider the parametric equations given by x(t) = 3t and y(t) = 2t + 1. Which of the followingaccurately describes the relationship between y and x?(A) y = 2?x+1/3(B) y...
- Q 1. A rocket is tossed from a platform and follows a parabolic path through the air. The height of therocket in meters is given by h(t) = -3t2 + 10t+8,...
- Q Find the following for the function f(x) = 4x + 2x - 4.(a) f(0)(b) f(4)(c) f(-4)(d) f(-x)(e) - f(x)(f) f(x + 3)(g) f(3x)(h) f(x + h)
- Q Iff(x,y) =5x - 2y/?x + y-7then the domain of is D= {(x,y)| x + y >7}Select one:TrueFalse
- Q In a study during the 1970's, it was found that one model of legislative turnover in the country A parliament was described by the following formulaM(t)=442e-0.05tIn this formula M(t) was...
- Q In the sale room at a store, every item is on sale for half the original price, plus 3 dollars. Complete parts a through d.(a) Write a function g that...
- Q In a mountain range of California, the percent of moisture that falls as snow rather than rain can be approximated by the function p(h) = 75 In (h) - 587,...
- Q (Lesson 32) The population of a town is decreasing at a rate of 1% per year. In 2000 there were 1300 people. Write anexponential decay function to model this situation....
- Q Express the quadratic function in factored form. Then determine the zeros, the equation of the axis ofsymmetry, the maximum/minimum value, the direction of opening and the coordinates of the vertex.f(x)...
- Q Out-of-pocket spending in a country for health care increased between 2004 and 2008. The function f(x)=2579 e 0.0359x models average annual expenditures per household, in dollars. In this model, x...
- Q What effect does the graph y = f(x) + k have on its parent function when k < 0?The graph is shifted upwards.The graph is shifted leftwards.The graph is shifted...
- Q Use a table of function values to approximate an x-value in which the exponential function exceeds the polynomial function.f(x)=3(4)^(2x-4)h(x) = (x+2)^3+1x = 4x = 2x = -3x = 0
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