Given f(x) = ax2 + k (where f(x) is a quadratic), describe when its reciprocal function...

Given f(x) = ax² + k (where f(x) is a quadratic), describe when its reciprocal function would and would not have vertical asymptotes. Refer to the values (+,-,0) of a and k in your description. What are all the possible scenarios?

Expert Solution

Colby Messinger answered 2 years ago

A quadratic function f is given. f(x) = x2 + 6x + 8 (a) Express f...

A quadratic function f is given. f(x) = x2 + 6x + 8 (a) Express f in standard form. f(x) = (b) Find the vertex and x- and y-intercepts of f. (If an answer does not exist, enter DNE.) vertex (x, y) = x-intercepts (x, y) = (smaller x-value) (x, y) = (larger x-value) y-intercept (x, y) = (d) Find the domain and range of f. (Enter your answers using interval notation.) domain range

Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)...

Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x) = x2 + 8x - 8

Consider the following growth function for fish given by F( X ) = rX(1 − X/K)...

Consider the following growth function for fish given by F( X ) = rX(1 − X/K) where the intrinsic growth rate r = 0.2 and the carrying capacity K = 100 tons of fish. Let the harvest function be given by H = qEX where the catchability coefficient be q = 0.01 and H is harvest in tons of fish. Compute the following: a. The maximum yield of fish at the steady state. b. Effort and Harvest when the price...

Consider the following production function: x = f(l,k) = lb kb where x is the output,...

Consider the following production function: x = f(l,k) = lb kb where x is the output, l is the labour input, k is the capital input, and b is a positive constant. Suppose b < 1/2. (a) Set up the cost minimization problem and solve for the conditional labour and conditional capital demand functions. Let w and r be the wage rate and rental cost of capital respectively. (b) Using your answer in (a), derive the cost function and simplify...

9. Given the function: f(x)=3x2+5x-17 a. find the interval where the function is increasing and where...

9. Given the function: f(x)=3x2+5x-17 a. find the interval where the function is increasing and where it is decreasing. b. Clearly state the critical number(s) of the function. c. Find the relative extrema of the function( using 1st derivative test). answer should be in (x,y) 10. Given the function: x3 - x2 + 52x - 17 a. determine the intervals where the graph of the given function is concave upward and where it is concave downward. b. Find any inflection...

PROBLEM: Given f(x)=4x - x2 + k & (1,3+k) on the graph of f. k =...

PROBLEM: Given f(x)=4x - x2 + k & (1,3+k) on the graph of f. k = 2 a) Write you equation after substituting in the value of k. b) Calculate the function values, showing your calculations, then graph three secant lines i. One thru P(1,f(1)) to P1(0.5,__) ii. One thru P(1,f(1)) to P2(1.5,__) iii. One thru P1 to P2 c) Find the slope of each of these three secant lines showing all calculations. d) NO DERIVATIVES ALLOWED HERE! Use...

Suppose a production function is given by F ( K , L ) = K 1 2...

Suppose a production function is given by F ( K , L ) = K 1 2 L 1 2, the price of capital “r” is $16, and the price of labor “w” is $16. a. (5) What combination of labor and capital minimizes the cost of producing 100 units of output in the long run? b. (5) When r falls to $1, what is the minimum cost of producing 100 pounds of pretzels in the short run? In the long...

2. Suppose a production function is given by F ( K , L ) = K 1...

2. Suppose a production function is given by F ( K , L ) = K 1 2 L 1 2, the price of capital “r” is $16, and the price of labor “w” is $16. a. (5) What combination of labor and capital minimizes the cost of producing 100 units of output in the long run? b. (5) When r falls to $1, what is the minimum cost of producing 100 pounds of pretzels in the short run? In the...

The production function is f(K,N) = N/2 + √ K, where N is the amount of...

The production function is f(K,N) = N/2 + √ K, where N is the amount of labor used and K the amount of capital used. (a) What is returns to scale of this production function? What is the marginal product of labor? (b) In the short run, K¯ = 4. Labor is variable. On the graph, draw output as a function of labor input in the short run in blue. Draw the marginal product of labor as a function of...

let f be the function on [0,1] given by f(x) = 1 if x is different...

let f be the function on [0,1] given by f(x) = 1 if x is different of 1/2 and 2 if x is equal to 1/2 Prove that f is Riemann integrable and compute integral of f(x) dx from 0 to 1 Hint for each epsilon >0 find a partition P so that Up (f) - Lp (f) <= epsilon

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