Functions Questions and Answers

Given f(x) = 5x+5 and g(x)=2x², first find f+g, f-g, fg, and f/g. Then determine the domain for each function. (f+g)(x) =... (Simplify your answer.)

A water balloon was launched into the air from the top of a hill 38 feet above ground. The balloon's path is represented by the equation h(t) = -16t² + 48t+ 38, where h(t) represents the height, in feet, and is the time in seconds. Find the average rate of change from the initial launch to the maximum height. A) 24 ft/sec Jamaica B) 28 ft/sec Huntington Beach C) 36 ft/sec Costa Rica D) 54 ft/sec Ireland E) 42 ft/sec Honolulu

Assume that a DVD loses 60% of its value every year it is in a video store. Suppose the initial value of the DVD was $80. B-46 HW eTool (Desmos). Homework Help a. What multiplier would you use to calculate the video's new values? b. What is the value of the DVD after one year? After four years? c. Write a continuous function, V(t), to model the value of a DVD after t years. d. When does the video have no value? e. Sketch a graph of this function. Be sure to scale and label the axes.

The Freedom Tower in New York City is 1776 feet tall. The equation f(t) = -16t² + 1776 models the height f(t) (in feet) of an object t seconds after it is dropped from the top of the tower. a. After how many seconds will the object hit the ground? Round your answer to the nearest hundredth of a second. (1 point) b. What is the height of the object 3 seconds after it has been dropped from the top of the tower? (1 point)

A can of soda is placed inside a cooler. As the soda cools, its temperature C() in degrees Celsius after f minutes is given by the following exponential function c(t)=23(0.93) Find the initial temperature. 20 °C Does the function represent growth or decay? O growth decay By what percent does the temperature change each minute? 6.99 %

Let f be the function whose graph is obtained by translating the graph of y = a. Write an equation for f(x) as a quotient of two polynomials. b. Determine the zero(s) of f. c. Identify the asymptotes of the graph of f(x). a. f(x) = (Simplify your answer.) to the right 5 units and up 4 units. CCCC

Evaluate the function f(x) = 6x +1 at the given values of the independent variable and simplify. a. f(-6) b. f(x+4) c. f(-x) a. f(-6)= (Simplify your answer.)

The function P(m) = 2m represents the number of points in a basketball game, P, as a function of the number of shots made, m. Given that the number of shots made is 40, find the number of points.

17. The half-life of the radioactive element plutonium-239 is 25,000 years. If 16 grams of plutonium-239 are initially present, how many grams are present after: (round your answer to the nearest hundredth) Find the exponential model first. a. 25,000 years b. 50,000 years c. 75,000 years d. 100,000 years e. 125,000 years

Refer to functions n and p. Find the function and write the domain in interval notation. Write any number in the intervals as an integer or a simplified fraction. n(x)=x+1 p(x)=x²-8x

If the X-intercepts of a quadratic graph are 3 and-5, which equation below best represents the graph? y = (x − 3)(x + 5) y = (x − 3)(x - 5) y = (x + 3)(x + 5) y = (x + 3)(x - 5)

When a factory operates from 6 AM to 6 PM, its total fuel consumption varies according to the formula f(t) = 0.5t² - 0.21t^0.4+ 13, where t is the time in hours after 6 AM and f(t) is the number of barrels of fuel oil. Step 1 of 3: How much fuel is consumed by 11 AM? Round your answer to 2 decimal places.

For f(x)=x² +5 and g(x)=x²-9, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(4); d. (gof)(4)

The logistic growth model P(t)=270/1+26e^-0.1681 represents the population of a species introduced into a new territory after t years When will the population be 60? A. 10.44 years B. 0.03 years C. 11.94 years D. 17.7 years

The growth of bacteria makes it necessary to time-date some food products so that they will be sold and consumed before the bacteria count is too high. Suppose for a certain product the number of bacteria present is given by f(t) = 500 e^0.11, where t is time in days and the value of f(t) is in millions. Find the number of bacteria present at each time. (a) 4 days (b) 5 days (c) 1 week

A plane loses altitude at the rate of 5 meters per second. It begins with an altitude of 8500 meters. The plane's altitude, A, is a function of the number of seconds, t, that pass. a. What is the independent variable in this situation? b. What is the dependent variable in this situation? c. Is this discrete or continuous data? d. Justify your reasoning.

6. After exercising, your heart rate can be modeled by R (t) = 151 e^-0.055t where 0 ≤ t ≤15 and t is the number of minutes that have elapsed after you stop exercising. a. Find your heart rate 10 minutes after exercising. b. How many minutes does it take your heart rate to drop to 70 beats per minute?

Select the expression below that properly sets up the partial fraction decomposition for the following rational expression: (x + 3)/(x³ + 9x²) Select the correct answer below: A/x² + B/x + 9 A/x³ + B/9x² A/x + B/x² + C/x+9 A/x + Bx/x² + (Cx + D / x + 9) A/x + (Bx + C / x² ) + D / x+9

Sketch the curve given by the set of parametric equations. X=t²+4 y=t/5+8

Suppose that the concentration of a bacteria sample is 30,000 bacteria per milliliter. If the concentration triples in 4 days, how long will it take for the concentration to reach 45,000 bacteria per milliliter?

World consumption of a certain metal is running at the rate of 346e^0.02t thousand metric tons per year, where t is measured in years and t = 0 corresponds to 2014. (a) Find a formula for the total amount of the metal that will be consumed within t years of 2014. C(t) = (b) When will the known world resources of 4300 thousand metric tons of the metal be exhausted? (Round your answer up to the next year.)

A state's income tax for a single person in a recent year was determined by the rule below, where x is the person's taxable income. 0.04x, if 0≤x≤6000 h(x)=240+0.05(x - 6000), if 6000 ≤x< 10,000 440+0.06(x-10,000), if x ≥ 10,000 Find the following function values and interpret the answers. (a) h(1020) (b) h(6590) (c) h(72,410) will get a tax refund of $ UB. An individual with a taxable income of $ OC. An individual with a taxable income more than $ will have to pay $ OD. An individual with a taxable income up to $ will have to pay $ (c) h(72,410) = $ (Round to the nearest cent as needed.) What can be inferred from the value of h(72,410)? (Round to the nearest cent as needed.). OA. An individual with a taxable income up to $ B. An individual with a taxable income of $ OC. An individual with a taxable income more D. An individual with a taxable income of $ as tax. will have to pay $ will have to pay $ than $ will have to pay $ will get a tax refund of $ as tax. as tax. as tax. as tax.

Brianna purchases a car. The value of the car is modeled by the function 25000(0.92)^t. Which statement below best describes the value the base 0.92? The car that Brianna purchased appreciates at a rate of 8%. The car Brianna purchased depreciates at a rate of 92%. O The car that Brianna purchased appreciates at a rate of 92%. The car Brianna purchased depreciates at a rate of 8%.

(1 pt) Find the critical points for the function f(x, y) = x³+y³ - 3x² - 12y + 2 and classify each as a local maximum, local minimum, saddle point, or none of these. critical points: (give your points as a comma separated list of (x,y) coordinates.) classifications: (give your answers in a comma separated list, specifying maximum, minimum, saddle point, or none for each, in the same order as you entered your critical points)

The parent function f(x) = x² is vertically compressed by a factor of and translated 11 units left and 5 units down. There is no correct answer given. g(x) = 2(x+11)² - 5 g(x) = 2(x-11)² - 5 g(x)=(1/2()x+11)²-5 g(x)=(1/2)(x-11)²-5

Solve the system of nonlinear inequalities by graphing each inequality and shading the overlapping region. Determine if the given point is a solutions to the system. That is, is the given point in the shaded solution region? y≤x²+6 y≥2x-1 Test (6,2) Yes No

A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = -3³ + 12t2 + 3t, where t represents the number of skincare items produced, in thousands. Today, the company produces 1 thousand products for a profit of $12 million. According to the graph of the function, what other quantity of product would result in the same profit? 5 thousand 4 thousand 3 thousand 2 thousand

An artifact was discovered by an archeologist, who intially estimated it to be about 1500 years old. Than, after carbon-14 analysis was completed, it was determined that the carbon-14 contained in the artifact decreased from 16 grams originally to 12 grams now, so that 75% of its original amount of carbon-14 remains. After the mathematical investigation was completed, this model was created: P(t) = 16e^-0.00012 where P(t) is the amount of carbon-14 remaining after 't' years. What conclusion should be made about the age of the artifact? 1) The initial estimate by the archeologist was not correct; the artifact is about 2300 years old. 2) The initial estimate by the archeologist was correct; the artifact is about 2300 years old. 3) The initial estimate by the archeologist was correct; the artifact is about 1500 years old. 4) The initial estimate by the archeologist was not correct; the artifact is about 25,000 years old.

Since the year 2005, defense spending (in millions of dollars) in the country of Warpeas can be approximately represented by the function: A(t) = 1.34e^0.11t Find the amount of defense spending in 2005 and describe (interpret) the change from one year to the next year. 1) Defense spending in 2005 was $1.34 million and changed by a multiple of about $1.12 million each year since 2005, meaning that the spending increased after 2005. 2) Defense spending in 2005 was $0.11 million and changed by a multiple of about $1.34 million each year since 2005, meaning that the spending increased after 2005. 3) Defense spending in 2005 was $1.34 million and changed by a multiple of about $0.11 million each year since 2005, meaning that the spending decreased after 2005. 4) Defense spending in 2005 was $1.34 million and did not change at all each year since 2005, meaning that the spending remained constant after 2005.

The function below gives the body concentration, in parts per million, of a certain dosage of medication after 't' hours. Find the horizontal asymptote and interpret what it means. y(t) = 0.8t+1000 51+4 t≥ 15 1) The horizontal asymptotte is y = 0.8 and this means that there are 0.8 parts per million of the medication dosage left in the body as t approaches infinity. 2) The horizontal asymptote is y = 0 and this means that there are 0 parts per million of the medication dosage left in the body as t approaches infinity. 3) The horizontal asymptote is y = 0.16 and this means that there are 0.16 parts per million of the medication dosage left in the body as t approaches infinity. 4) The horizontal asymptote is y = -0.8 and this means that there are -0.8 parts per million of the medication dosage left in the body as t approaches infinity.

Using the given cost function C(x) = 2850 +410x + 1.4x2, where C is total cost and is the number of units produced. The demand function p(x) = 1230, where p is the price charged per unit x. Find the production level that will maximize profit.

The fox population in a certain region had a relative growth rate of 6.5% per year since 1985. The population in 1985 was 450 foxes. Using the exponential growth model, find the fox population in 2006. 1) The population is 85982 foxes. 2) The population is 1762 foxes. 3) The population is 516 foxes. 4) The population is 3375 foxes.

A. Post your polynomials, f(x) and g(x), and submit screenshots of your organized calculations. • Answer the following questions: • Why did you choose the method you used to solve g(-2)? • Can you think of any other ways (other than the three used here) to evaluate a function? • Can you come up with and explain a way to check your answer? • Challenge: Can you explain why the remainder theorem

Suppose that a function f is odd over it's domain (-∞,∞) and that f(-3)=5 is a local maximum. Which of the following statements must be true? A. f(3) = -5 is a local minimum value. B. f(3)=5 is a local maximum value. C. f(-3) = -5 is a local minimum value. D. f has only one local extrema

Choose the definition below that best describes what is changed in the graph by changing the value of C in the equation f(x) = A sin (Bx-C)+D. PHASE SHIFT. The number of units the graph has been shifted in the horizontal direction from its usual position. AMPLITUDE: The height of the function from its mid-line. VERTICAL SHIFT: The number of units that the graph has been shifted in the vertical direction from its usual position. PERIOD: The shortest repeating portion of the graph is called a cycle. The horizontal length of each cycle is called the period.

Henrietta did an experiment. She started out with 800 bacteria cells. She found that the growth rate of the bacteria cells was 3.2%. Sketch the graph that represents the situation. Label the y-intercept and the point that represents the projected bacteria population 35 h from the time Henrietta started the experiment.

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second. y = -16x² + 170x + 61

For the function defined below, use a graphing calculator to find a comprehensive graph and then answer parts (a) through (g) below. P(x)=2x+3x³-18x²-7x-60 (Type your answer in interval notation. Type integers or decimals rounded to the nearest hundredth as needed.) (e) Determine all intercepts. Determine the y-intercept analytically. Select the correct choice below and fill in any answer boxes in your choice, if necessary. A. The x-intercept(s) is/are and the y-intercept(s) is/are (Type an integer or decimal rounded to the nearest hundredth as needed. Use a comma to separate answers as needed.) B.The x-intercept(s) is/are and there are no y-intercepts. (Type an integer or decimal C. The y-intercept(s) is/are and there are no x-intercepts. (Type an integer or decimal rounded to the nearest hundredth as needed. Use a comma to separate answers as needed.) D. There is no x-intercept or y-intercept.

Given the cost function C(x) and the revenue function R(x), find the number of units x that must be sold to break even. C(x) = 14x+20,000 and R(x) = 16x. How many units must be produced and sold in order to break even?

Determine the smallest degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001. f(x) = e^x, approximate f(-0.35)

How is the function g(x) = sin(x) + 3 transformed from the parent sine function, f(x) = sin(x)? The period of f(x) is increased by 3 to create g(x). The midline of f(x) is shifted down by 3 to create g(x). f(x) is shifted right by 3 to create g(x). The midline of f(x) is shifted up by 3 to create g(x).

The tolerance for a ball bearing is 0.02. Per Manufacturing specifications, the true diameter of the bearing is to be 5.8 centimeters and the measured value of the diameter is x centimeters. Write this statement in plain English using mathematical language; then, write it symbolically using absolute value notation; use the variable x for the score. Lastly, give us the range of the measured values.

A bacteria culture contains 1300 bacteria initially and doubles every hour. (a) Find a function / that models the number of bacteria after t hours. N(t) = (b) Find the number of bacteria after 24 hours. bacteria

Find the exact area enclosed by the curve y = x²(4- x)² and the x-axis. Area

The LaTique Outlet store estimate that their weekly sales S and weekly advertising cos t x is modeled by the equation S(x) = 60000 - 40000e-0.0005x The present weekly advertising cost of $2,000, is now increa sin g at a rate of $300 per week. What is the current rate of change of sales in dollars per week?

Find a polynomial of the specified degree that has the given zeros. Degree 4; zeros -3, 0, 3, 5 P(x) =

Consider the interval [-16, 14]. (a) Find the length of the interval. 30 (b) If we partition [-16, 14] into 10 subintervals of equal length, then (i) the length of each subinterval is 3 (ii) the first subinterval is [-16, - 13] (iii)the midpoint of the first subinterval is -14.5 (iv) the midpoint of the second subinterval is -11.5

When a certain medical drug is administered to a patient, the number of milligrams remaining in the patient's bloodstream after t hours is modeled by D(t) = 90e^-0.1t How many milligrams of the drug remain in the patient's bloodstream after 3 hours? (Round your answer to one decimal place.) mg

Consider the following function. g(x) =-2/3 x^3 Step 2 of 2: Find two points on the graph of this function, other than the origin, that fit within the given [-10, 10] by [-10, 10] grid, Express each coordinate as an integer or simplified fraction, or round to four decimal places as necessary.

Suppose a product's revenue function is given by R(q)=-6q² +700g. Find an expression for the marginal revenue function, simplify it, and record your result in the box below. Be sure to use the proper variable in your answer. (Use the preview button to check your syntax before submitting your answer.) Answer: MR(q)=