Stretch1. Consider the graph of a cubic function.a. Determine a quadratic function thatcould have been dilated to produce thecubic function. State the function usedto dilate the quadratic function.b. Determine a linear function that couldhave been dilated to produce the cubicfunction. State the function used todilate the linear function.2. Consider the function f(x)= x³ + 2x² - 5x - 6.a. Use technology to graph the function,and then sketch it on the grid.b. Determine the domain and range ofthe function.c. Determine the intervals over which thefunction is increasing and decreasing.d. Determine the x- and y-intercepts of thegraph of f(x).e. Determine the values of x for whichf(x) = -4.-8 -6 -4-8-6A-4-2ty86-42--4--202-6--8-ty1612-8-st4--4--8-0-12--16244668·008Ax**

Answered: Image /qna-images/answer/8d2036bc-4d04-4ebe-b3ac-725786db71ea.jpg

Answered: 1. Consider the graph of a cubic…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Write the cubic function represented by the graph
2. Sketch the graph of the function ƒ (x) = 2x² – 5x + 2. Label all intercepts. 3. A taxi company charges $5.00 for the first quarter mile and $0.60 for each additional quarter mile. Find a linear function F for the total fare in dollars, given x, the number of miles. Graph this function. 4. The height hin feet of a projectile fired up from the ground is given by the function h(t) = −16t² + 128t, where t it the time in seconds. How many seconds will it take the projectile to reach its maximum height? What is that height? How many seconds will it take for the projectile to land?
…
Find an example of a quadratic function in the field of your interest. Draw its picture in the coordinate plane. Find its vertex, x-intercept(s), y-intercept, and max or min value and explain what they represent in your problem
d. Use regression in Desmos to find the best linear function of the form y = mx + b to model the data. Write down the function that Desmos gives you (use the correct variables in your written answer). Use regression in Desmos to find the best quadratic function of the form y = a(x – k)² + h to model the data. Write down the function that Desmos gives you е. (use the correct variables in your written answer). f. Do you think your linear model, quadratic model, or your exponential model is a better fit to the data? Explain your reasoning.
+ 3. An amusement park is planning a new roller coaster. Part of it is to have the shape of the cosine function. The high and low points of this part differ by 24 meters and cover a horizontal distance of 40 meters from the high point to the low point. The low point is 6 meters below ground in a tunnel. Let y repre- sent the number of meters the track is above or below ground, and let x repre- sent the number of meters the track is horizontally from the high point. a. Sketch this situation. b. The equation y = 12 cos (4.5x) + 6 models the situation when x and y are in meters and 4.5 is in degrees per meter. Rewrite y = 12 cos (4.5x) + 6 as an equation for which the coefficient of x is in radians per meter. c. What is the length of a vertical support girder at the high point? At a dis- tance of 6 meters horizontally from the high point? At a distance of 20 meters horizontally from the high point? d. Measured horizontally, how far from the high point does the roller coaster enter the…
4. A company is told that when manufacturing 201 vehicles, it will minimize its production costs per vehicle to be $3015. If the company only manufactures 2 vehicles, the cost per vehicle is $82,217. Write a quadratic function representing the cost per vehicle C in terms of the number of vehicles manufactured v. Give final answer in Quadratic Form (not Transformation Form). Show work. Function:
the percentages of people in a country who say they are happy are shown in the table for various year. Let f(t) be the percentage of people in a country who say they are very happy at t year since 1970. complete part a-d below. year percentage 1972 34 1980 36 1990 43 2000 41 2010 29 a. find a quadratic equation of t in vertex form. b. Find ( 47) and what does it mean in this situation c. find when f(t)=24 and what does it mean d. what is the vertex of the model? and what does it mean
The table below shows data on the number of employees that a small company had from 1975 to 2000. Year 1975 1980 1985 1990 1995 2000 # of 50 65 70 60 55 44 Employees Let 0 represent the year 1975. Find a quadratic model for this function. .2 y = ax + bx + c Using the above equation, fill in the coefficients for a, b, and c rounding all decimals to the hundredths place.

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