Basic Math question and answers for November 02, 2024
- Q Find the domain of the rational function.f(x) 1 - 3x x-10x+16All real number except -8 and 2All real numbers except 8, 2, 1 3, and 0All real numbers except 8...
- Q Select the range and y-intercept of: f(x) = 5^x - 2(Choose 2)y ? (-?, ?)y ? (-2,?)x ? (-?,?)y ? (-?, 2)(0,0)x ? (0, 2)(0,-1)
- Q Find the vertex: f (x) = x + 6x + 5(2,21)(-3,-4)(3, 32)(-4,-3)
- Q Justin has 3 skateboards and plans to purchase 2 more skateboards each month. Does this situation model a linear or exponential function?ExponentialLinear
- Q Part AWould kind of line would you use to graph the linear inequality: y ?2x-4Part BWhere would you shade the solutions to the linear inequality: y ? 2x - 4
- Q Find the inverse function for the following: f(x) =2+3x /5x and use your result to show that f(f-(x)) = x.(HINT: f(f-(x)) is just function notation....you are being asked to replace...
- Q To demonstrate your understanding of the "mathematical language" used in this course, give anexample of each of the following.(a) a square root function that has been vertically stretched by a...
- Q What is the result of adding the system of equations?2x + y = 43x-y=6x=10x=25x=10
- Q Find the inverse of f(x) =5x- 3/x-1
- Q What are the domain and range of the relation? Is the relation a function?F=((85,-16), (15,2), ( 109,2), (70,42)}
- Q Let (x) = (x + 6).Restrict the domain off to a non-decreasing interval. Now find the inverse of f
- Q Find the domain, any asymptotes, and the x- and y-intercepts of f(x). Then graph the function.f(x)=2x+3/x
- Q For the function f(x), find the maximum number of real zeros, the maximum number of x-intercepts, and the maximum number of turning points that the function can have.f(x)=x4-x +6
- Q Suppose that poaching reduces the population of an endangered animal by 8% per year.Further suppose that when the population of this animal falls below 30, its extinction isinevitable (owing to...
- Q Determine if f(x) x5/4 - x + 1 is a polynomial function. If it is, state the degreeand the leading coefficient. If not, state why.No. There is an exponent on...
- Q Let D= (x) x is the height above the ground) be the domain, and let f(x)= "time spent on a Ferris wheel" be the possible function. Determine if the relation...
- Q The position (in feet) of a buoy in the water can be modeled by the functions(t) = 9 cos(t) where t is the elapsed time in seconds.(a) If we start...
- Q Choose all that are properties of one-to-one functions.x-values are repeated.Functions are always one-to-one.The graph passes the vertical line test.y-values are repeated.y-values are not repeated.x-values are not repeated.The graph passes the...
- Q a. Find the slant asymptote of the graph of the rational function.b. Follow the seven-step strategy and use the slant asymptote to graph the rational function.f(x)=x^2-49/xa. Select the correct choice...
- Q The function graphed to the right is of the form y = c + cos x, y = c + sinx,y = cos (x-d), or y = sin (x-d), where...
- Q Describe how the graph of g(x) =1/x+6 - 2 can be obtained from the graph of f(x) = 1/x.How can the graph of g(x)= 1/x+6 -2 be obtained from the...
- Q For f(x) = 6x and g(x)=x+9, find the following functions.a. (fog)(x); b. (gof)(x); c. (fog)(2); d. (gof)(2)a. (fog)(x) =
- Q Determine whether the function is even, odd, or neither. Then determine whether the function's graph is symmetric with respect to the y-axis, the origin, or neither. f(x)=x+x+1Determine whether the function...
- Q Find and simplify each of the following for f(x) = 8x - 9.(A) f(x + h)(B) f(x+h)-f(x)(C)f(x+h)-f(x)/h
- Q If f(x) = x+3, what is the ordered pair for f(7)?A (10,7)B (7,4)C (7,10)D (4,7)
- Q Describe a function g(z) in terms of f(x) if the graph of g is obtained by vertically stretching f by a factorof 7, then shifting the graph off to the...
- Q f(x) = -5(x + 4)(x ? 3)(x + 1)a. How does the graph behave with relation to the x-axis at x=-1?b. What are the real zeros of the function?c. What...
- Q f(x) = 4x(x + 3)(x - 2)5(x + 6)a. How does the graph behave with relation to the x-axis at x = -6?b. What are the real zeros of the...
- Q If f(x) is an odd function, which statement about the graph of f(x) must be true?It has rotational symmetry about the origin.It has line symmetry about the line y =...
- Q Consider the recursive function.f(1) = 2f(n) = 5 f(n-1), for n ? 2Which statement is true?A The value of f(6) is 2 times the value of f(3).B The value of...
- Q The parent square root function, f, is transformed to create function g.g(x)=?+3-4Which statement is true?A The graph of fis translated 3 units to the right and 4 units up.B. The...
- Q Consider these functions:f(x)=3x + 2g(x)=3?(x-2)/3Which statements, if any, are true about these functions?1. The function g(x)) = x for all real x.II. The function g(x)) = x for all real...
- Q Which statement is true about the graph of function f?f(3) = log? #A The graph has a horizontal asymptote of y = 0 and is decreasing as x approaches positive...
- Q The domain, range, and intercepts of a function are shown. Which set of information could be characteristics of the function's inverse? range: y2-1x-intercept: (8,0)domain: x2-2y-intercept: (0,4)A. domain: x2-1; range: yz...
- Q Determine whether the function is even, odd, or neither. Then determine whether the function's graph is symmetric with respect to the y-axis, the origin, or neither.f(x)=x5 +6xDetermine whether the function...
- Q Which statement best describes the end behavior of the following function?F(x) = 2x-x +5x-9A. The graph of the function starts low and ends low.B. The graph of the function starts...
- Q Select all that describe the graph of f(x) = 1/3 4x as compared to the graph of f(x) = 4xvertical compressionexponential growthreflected over the y-axisreflected over the x-axisvertical stretchexponential decay
- Q Select the equations that represent an Exponential Growth Equation.(Choose 2)f(x) = 1/3(1/2) xf(x) = 2(1/5)xf(x) = 1/5(3/2)xf(x) = 2(3)x
- Q Select all that describe the graph of f(x) = 3(1/2)x-4-2 as compared to f(x) = ()*.(Choose 3)horizontal shift to the right 4Overtical compressionvertical stretchvertical shift up 2vertical shift down 2horizontal...
- Q f (x) = (1/5)x represents an exponential growth equation.O TrueO False
- Q What is the output of the following function for x = 2? F(x) = 2x - x +5x-9A. 25B. 11C. 9D. 14
- Q What are the domain and range of the function represented by the set ofordered pairs?{(-13, 9), (-7,-5), (5, 14), (11, -10)}A. Domain: {-13, -7, 5, 11}Range: (-10,-5, 9, 14)B. Domain:...
- Q Use the quadratic formula to solve the equation: x + 3x - 5 = 0x = -5 + ?13/2 or x = -5-?13/2x = -3+?29/2 or x = -3-?29/2x =...
- Q f(x)=?x - 11. Find the inverse of f(x) and its domain.A. f(x) = x +11; x2-11B. (x) = (x + 11) ; x ? 0C. (x) = x...
- Q Which pair of functions are inverses of each other?A. f(x) = 7/x - 2 and g(x) = x+2/7B. f(x) = x/7 + 10 and g(x) = 7x - 10C. f(x)...
- Q For - 11 ? x ? 13 the function f is defined by f(x) = x (x + 1)On which two intervals is the function increasing (enter intervals in ascending...
- Q f(x) = 4x + 3x - 2g(x) = 6x 3x - 4Find (f + g)(x).A. (f+g)(x) = 10x - 6B. (f+g)(x) = 6x + 7x + 3x + 2C. (f+g)(x)...
- Q A trigonometric function models the monthly rainfall of a city, which reaches a maximum monthly rainfall of 8 inches in the spring and fall and a minimum monthly rainfall of...
- Q A retailer is having a promotional sale for 35% off all items. There is a 7% sales tax added to the price. Which represents the situation, where x is the...
- Q For the real-valued functions g(x)=x+3 and h(x)=x-4, find the composition goh and specify its domain using interval notation.
- Q Which function displays this end behavior?As x approaches negative infinity, y approaches negative infinity.As x approaches positive infinity, y approaches negative infinity.A y = (2x)^1/3 - 7B. y = -3x^2...
- Q The functions f and g are defined by f(x) = 8x +33 and g(x) = 2 - (1.2).1. Which function eventually grows faster, for g? Explain how you know.2. Explain...
- Q Write a rule for g that represents the indicated transformations of the graph of fg (z) = A tan B (x - C) + D(x) = 1/6 tan (x): Translation...
- Q Consider a function f(x) = x. A second function h(x) is the result of reflecting f(x) across the x axis and translating it 3 units in the positive y-direction (upward)....
- Q Using interval notation, identify the domain for the function: f(x)=2x+1/ x-4(-?,?)(-?,4)U(4,?)(-?,-4)U(4,?)(-?,2)U(2,?)
- Q Use the remainder theorem to find P (3) for P(x) = -x + 3x-x+5.Specifically, give the quotient and the remainder for the associated division and the value of P (3).
- Q A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then...
- Q Which of the following functions have an amplitude of 4 and a period of 2? Select all that apply.y = 4 cos 2xy=2 sin 4xy = 4 ?os ?x
- Q Find the difference quotient f(x+h)-f(x)/h where h#0, for the function below.f(x)=-3x+6x-9Simplify your answer as much as possible.
- Q For the real-valued functions f(x)=?2x+4 and g(x)=x-1, find the composition f.g and specify its domain using interval notation.(f.g)(x) = Domain of f g :
- Q The functions f and g are defined as follows.f(x)=x-x-2 and g(x)= 7x-3/5x-1Find f(x+8) and g(x/4)Write your answers without parentheses and simplify them as much as possible.
- Q The functions f and g are defined as follows.f(x)=x+9x+5 and g(x)= 3/ x-2Find f(x-3) and g(-/x)
- Q The functions f and g are defined as follows.f(x)=4x+3/5x+2and g(x)=?x^2-8xWrite your answers without parentheses and simplify them as much as possible.Find f(1/x)and g(x-2).
- Q The area A (r) (in square meters) of a circular algae colony with radius r meters is given by A (r) =?r.The radius M (t) (in meters) after t minutes...
- Q Use interval notation to represent all values of x satisfying the given conditions.f(x) = 5x-4, g(x) = 4x-6, and f(x) > g(x)A. (-10,00)B. (-?0.-2]C. (-2,00)D. [-2.00)
- Q Write the quadratic equation with the following transformations:Reflected over the x-axisVertical shrink of 1/3Translated up 2 unitsy = -3(x + 2)y = -(1/3)x + 2y = -(1/3)(x + 2)y =...
- Q Let f(x)=x-4x+7x-6/x-2a. Graph the function on the window xmin = -2, xmax = 4, ymin = 0,ymax = 10.b. What is the domain of the function?c. Find lim x?2 f(x).d....
- Q Find each indicated quantity if it exists. Let f(x) = |x-11| / x-11 .Complete parts (A) through (D).(A) Select the correct choice below and, if necessary, fill in the answer...
- Q The equation y = 8x + 12, where x is the number ofhours and y is the total cost, represents what the surfinstructor charges for lessons. Use this information todescribe...
- Q The graph of:y = 11x + 22x + 14x / (5x + 1)(11x + 7)has one vertical asympote and one horizontal asymptote.An equation for the vertical asymptote is:An equation for...
- Q 9/7x+35=9/x+5-6/7 aWhat is/are the value or values of the variable that make(s) the denominators zero?x=(Simplify your answer. Use a comma to separate answers as needed.)b. Select the correct choice below...
- Q For the function g(x)=1/2x-4, find g(2) + g(a).g(2)+g(a) = (Use integers or fractions for any numbers in the expression.)
- Q Victoria read a 160-page historical fiction novel followed by a science fiction novel of the exact same length. Her average reading speed of the science fiction novel was 2 pages...
- Q Enter the correct answer in the box.The graph of function g is created by applying these transformations to the parent tangent function:reflection over the x-axis horizontal stretch by a factor...
- Q The exponential function f(x) = 2500(0.4) models the amount of money in Zachary's savings account over the last 10 years. Is Zachary's account balance increasing or decreasing? Write the base...
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