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Graphs and Functions

Value of function at a given point

1. The number of 4-year college, public and private, in the period 1980-1996 can be modeled by f(x)=0.0003x^3 - 0.007x^2+0.058x+1.957 0 less than or equal to X less then or equal to 16 Where X is the number of years since 1980 and f(x) is the number of 4-year colleges measured in thousands. Determine the average number

graph the functions with data points

For the function, y = ___1____ x - 2 a) Give the y values for x = -2, -1, 0, 1, 2, 3. Answer: Show work in this space. b) Using these points, draw a curve. Show graph here.

Graphs and Solving Linear Equations Word Problems (20 Problems)

Solve the following equations for the unknown. 1. 5x = 20 2. 7x - 3 = 18 Graph the following equations; calculate the slope, x-intercept, and y-intercept, and label the intercepts on the graph. 3. y = x + 3 4. y = -2x - 7 5. 2x + 3y = 9 6. A consumer electronics c

Break even analysis: Labor intensive firm and capital intensive firms

Draw two break-even graphs-one for a conservative firm using labor-intensive production and another for a capital-intensive firm. Assuming these companies compete within the same industry and have identical sales, explain the impact of changes in sales volume on both firms' profits. Although no example is provided in the

Equations of Straight Lines

1. Graph line with equation y=-4x-2. 2. 2x=8y=17=0 3. Graph the line with slope -2 passing through the point (-3,4). 4. Find slope of the line graphed (-44, 28) (9, -12). 5. x=9 graph the line 6. 6x-9y+7=0. 7. 2x=5y+3 8. Write an equation of line (0, -4). 9. A line passes through the point (6, -6

Asymptotes, Descartes's Rule and coordinates of the vertex

1. f(x) = x^3 + x^2 - 4x - 4. (a) What is the end behavior of this function? (Does it go up or down to the left? Does it go up or down the right?) (b) What is the maximum number of turning points for this function? 2. Give the coordinates of the vertex of the parabola y = (x + 2)^2 + 5. 3. Use Descartes's Rule of Sig

Simplifying and Solving Equations with Exponents

1. Simplify the expression using properties of exponents. Answer should contain positive exponents only. (3x^2y^3)^2(3xy)^2 / (2x^4y^3)^-3 2. Solve for X: 3/x - 1/x+2 = -2/3x+6 3. Use the quadratic formula to solve for x: x^2 -4x + 2 = 0 4. Solve for x by factoring: x^3 + x^2 - 6x =

One-to-One and Onto Functions

Suppose that X and Y are finite sets, with m and n elements respectively. Suppose further that the function f : X → Y is one-to-one and the function g : X →Y is onto. (i) Use the function f to show that m ≤ n. (ii) Use the function g to show that m ≥ n. (iii) Is f : X → Y onto? Justify your assertion. (iv) Is th

Input-output Tables and Equations of Lines, Slope and Intercept

Decide whether the relation is a function. 1- (6,5), (4,3), (-2,3), (0,-1) , (-1,2), (-4,-5), (-3,4) 2- (4,4), (3,3), (-1,1), (6,6), (1,-2) make an input-output table for the function rule. Use a domain of -10,-5,0,5, and 10. Identify the range. y=8x+1 y=-6x y=x square 2+5 write a function that relates and x and

Algebra Description Graphed

Please answer the following questions ASAP: Match each description of a graph with an equation. The graphs are all described in relation to the graph y = x^2 shifted 3 units upward shifted 3 units to the left shifted 3 units downward stretched out and flipped upside down shifted 3 units to the right

Quadratic function

Given the quadratic function (see attached file) a.) Does the graph open up or down? b.) What is the equation of the axis of symmetry? c.) What are the coordinates of the vertex? d.) Give the y intercept e.) Give the x intercept(s) f.) sketch the graph

Math problems help

1. Find an equation of variation where y varies jointly, directly as the cube of x and cube root of z, and inversely as the square of w, and y = 4 when x = 2 and z = 8 and w = 4. 2. Perform the indicated operation and simplify. y2 + 3y y2 -y y - 1 y2 -5y + 6 (y-3)(y+2)

Rational function

For the rational function (see attached), give the intercepts and asymptotes and sketch the graph.

Derivative Implicit Functions

(See attached file for full problem description with proper equations) --- The problems need to be solved in full and to show all work 1a) Find the following derivative implicitly with respect to x If, Y=(1+xy)^(1/xy). Find dy/dx! without simplifying the derivative. Compute dy/dx at (1, 1). b) find the formul

Revenue Functions Models

3. Let be a function that models the temperature change in a certain valley from 6:00 PM one day to 8:00 AM the following morning. Let the origin represent the temperature at 6:00 pm. ________________ ________________ a. Find, and then sketch, the first and second derivatives of on

Distance As A Function Of Time

Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0 · 16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2). · v0 is the initial

Ploting a Quadratic Function

For the function y = x2 - 4x - 5, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is the line of symmetry? c) Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x - h)2 + k. d) Describe how this graph compares

Quadratic Functions

1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks: a) Solve by factoring. b) Solve by completing the square. c) Solve by using the quadratic formula.

Graphing

(See attached file for full problem description with diagrams) --- ? For non-integer answers, use a fraction rather than a decimal. ? Include o the formula with substituted values. o the final calculated answer with units. a) Given the above graph, identify the graph of the function (line, parabola, hyperbola, o

Graphs and Linear Functions

Please see the attached file for the fully formatted problems. --- - How do I find the formulas with substituted values and show the final calculated answer with units? - I have also highlighted in yellow what needs to be shown for each problem. 1) a) How do I identify the graph of the function (line, parabola, hype

Polar and Parametric Equations : Eliminate the parameter to find a cartesian euqation of the curve; sketch the curve with the given polar equation. Show the equation for the sketch.

1,2,3) a) Sketch the curve by using the paramtric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. b) Eliminate the parameter to find a cartesian euqation of the curve. 1)x = 3t-5, y=2t + 1. Part a is just making a table using t and solving for x and y, but whe