Functions Questions and Answers

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)=

6. A football player attempts to kick a football over a goal post. The path of the football can be modeled by the function h(x)= 1/225x² + 2/3x, where x is the horizontal distance from the kick, and h(x) is the height of the football above the ground, when both are measured in feet. a. [4 pts] On the set of axes below, graph the function. Make sure to clearly label your graph.

Suppose that an object that is originally at room temperature of 40°C is placed in a freezer. The temperature T (x) (in °C) of the object can be approximated by the model T (x)= 440 / (x² + 4x + 11) where x is the time in hours after the object is placed in the freezer. (a) What is the horizontal asymptote of the graph of this function and what does it represent in the context of this problem? The horizontal asymptote is y = and means that the temperature will approach°C as time increases without bound.

For g(x)=(x-8)(x - 9)(x + 3), find all x-values for which g(x) > 0. Select the correct choice below and, if necessary, fill in the answer box to complete your answer. A. The solution set is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. The solution is all real numbers. C. There is no solution.

Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema. f(x) = -x³-3x² + 9x + 2 Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. There are no relative maxima. The function has a relative minimum of (Use a comma to separate answers as needed.) B. The function has a relative minimum of at x = (Use a comma to separate answers as needed.) C. There are no relative minima. The function has a relative maximum of at x = (Use a comma to separate answers as needed.) D. There are no relative extrema. at x = and a relative maximum of at x =

Eric and his wife are each starting a saving plan. Eric will initially set aside $250 and then add $135 every month to the savings. The amount A (in dollars) saved this way is given by the function A = 135N+250, where N is the number of months he has been saving. His wife will not set an initial amount aside but will add $585 to the savings every month. The amount B (in dollars) saved using this plan is given by the function B = 585N. Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N. Simplify your answer as much as possible.

Jesaki Publishing is planning for a new novel, and figures fixed costs (overhead, advances, promotion, copy editing, typesetting) at $65,000, and variable costs (printing, paper, binding, shipping) at $1.60 for each book produced. The book will be sold to distributors for $12 each. Answer the following questions about this venture. Let x be the number of books produced. The cost function is C(x) = mx + b,. for some values m and b, where C(x) is given in dollars. Round m and b to the nearest tenth (1 decimal place). What is the total revenue if Jesaki Publishing breaks even? Round to the nearest dollar.

The doubling period of a bacterial population is 20 minutes. At time t = 80 minutes, the bacterial population was 70000. What was the initial population at time t = 0? Find the size of the bacterial population after 3 hours.

Select the statement that explains one differences between the graphs of f(x) = 5x² and g(x)=1/5x2 The graph of f(x) is wider than the graph of g (x). The graph of f(x) is narrower than the graph of g (x). The graphs open in opposite directions. The y-coordinate of the vertex of f(x) is greater than the y- coordinate of the vertex of g (x).

A small publishing company is releasing a new book. The production costs will include a one-time fixed cost for editing and an additional cost for each book printed. The total production cost C (in dollars) is given by the function C= 750+19.95N, where N is the number of books. The total revenue earned (in dollars) from selling the books is given by the function R = 34.60N. Let P be the profit made (in dollars). Write an equation relating P to N. Simplify your answer as much as possible.

Suppose the polynomial function below represents the power generated by a wind turbine, where x represents the wind speed in meters per second and y represents the kilowatts generated. Interpret f(10). f(x)=0.08x³+x²+x+0.26

A baseball is thrown vertically upward at a rate of 105 feet per second from an initial height of 5 feet. Use the projectile formula - 16t² + vot + ho to determine when the height of the ball will be 168 feet. [Recall that vo is the initial velocity of the object and h0 is the inital height of the object.] Answer: The baseball is at 168 feet after feet/seconds/feet per second Note: Round any numerical responses to two decimal places. If answers, separate them with commas.

For f(x)=x+4 and g(x) = 2x + 2, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d. (gof)(2) a. (fog)(x) = (Simplify your answer.)

A shipping company charges fees according to the weight of a package. Prices follow the function below. 2.80 for 0<x< 1.5 y ={ 2.90 for 1.5 < x < 2 } 3.00 for x ≥ 2 What is the cost to ship an item that weighs exactly 1.5lbs?

The lacrosse team is raising money by selling cheesecakes. The players plan to sell an entire cheesecake for $24.00 each and slices of cheesecake for $3.50 each. If they want to raise at least $700, how many of each could they sell? Part A: List three possible combinations of entire cheesecakes and slices of cheesecake the players could sell to reach their goal of raising at least $700. Part B: Write an inequality to represent the situation. Part C: Graph the inequality and shade where the solutions are. Part D: What is the difference in the amount of money raised for ordered pairs falling on the line and the ones that fall in the shaded area? Part E: What do the x- and y-intercepts represent?

Select the correct answer. Rodrigo is tracking the number of visitors at two parks. He created these functions to model the total number of people visiting each park, where x is the number of hours after sunrise. West Park: A(z) = -0.683 + 7.052 +3.25 + B(r) = -2.0812² +221 + 5 East Park: Which function models the total number of visitors at both parks each hour after sunrise? OA T(T) = -0.683 +4.971² + 25.25 +5 OB. T(T) = -2.7613 +29.05x2 + 8.25 OC. T(T) OD. T(T) = -0.683 +9.13r2 +221 + 8.25 = -2.76x3 +7.05x2+25.25 +5

A function is given. f(t) = ²/-; (a) Determine the net change between the given values of the variable. t = a, t = a + h (b) Determine the average rate of change between the given values of the variable.

The average annual cost (in dollars) for health insurance in a country can be approximated by the function g(x)=1736.3 + 1661.3 In x, where x=6 corresponds to the year 2006. (a) Estimate the average cost in 2011. (b) Graph the function g for the period 2006 to 2015 (c) Assuming that the graph remains accurate, what does the shape of the graph suggest regarding the average cost of health insurance?

A chain-saw rental firm charges $21 per day or fraction of a day to rent a saw, plus a fixed fee of $9 for re-sharpening the blade. Additional portions of a day are considered to a be a full day's rental, so rounding upward to identify an entire rental period may be necessary. Let S(x) represent the cost of renting a saw for x days. Complete parts (a) through (m) below. A. Draw a line through each open circle. B. Draw a line through each closed circle. C. Find the cost of renting a saw for more than 2 days and less than or equal to 3 days and graph the amount. Do the same for all days and fractions of days. D. Find the total number of days someone could rent a saw for and end the y-axis at that point. Continue to graph functions until the maximum. (i) What is the independent value? A. S; the cost of renting a saw B. The fixed cost of re-sharpening the blade C. x; the number of full and partial days D. The number of saws that are rented per day

Mrs. J bought a rare painting in 2000 for $150,000. The value of the painting increases at a rate of 3% per year. How much is the painting worth in 2025? First, write an equation that represents the value of the painting, V, after x years. Then calculate how much the painting is worth in 2025. You must use the equation that you set up and show what you typed into your calculator in order to earn full credit. round your answer to the nearest whole dollar.

Evaluate the function f(x)=x² + 8x + 7 at the given values of the independent variable and simplify, a. f(6) b. f(x+8) c. f(-x)

The first year Eleanor organized a fund-raising event, she invited 30 people. For each of the next 5 years, she invited double the number of people she had invited the previous year. If f(n) is the number of people invited to the fund-raiser n years after Eleanor began organizing the event, which of the following statements best describes the function f? A) The function f is a decreasing linear function. B) The function f is an increasing linear function. C) The function f is a decreasing exponential function. D) The function f is an increasing exponential function.

In 2010, the population of Greenbow, AL was 1,200 people. The population has risen at at rate of 3% each year since. Let x = the number of years since 2010 and y the population of Greenbow. What will the population of Greenbow be in 2020? Write the equation, using the variables above, that represents this situation and solve the problem, showing the calculation you did to get your solution. Round your answer to the nearest whole number.

What is the equation for a cosecant function with vertical asymptotes found at x = pi/4 +pi/4 n, such that n is an integer? f(x) = 2cscx g(x) = 4csc2x h(x) = 2csc4x j(x) = 4cscx

The size P of a small herbivore population at time t (in years) obeys the function P(t)-900e0.15t if they have enough food and the predator population stays constant. After how many years will the population reach 1800? 4.62 yrs 45.35 yrs 11.29 yrs 14.65 yrs

Find the average rate of change of f(x)=x² - 4x + 4 over the following intervals. (a) From 3 to - 2 (b) From 1 to 4 (c) From 4 to 5 (a) The average rate of change from 3 to - 2 is

Given the toolkit function f(x) = x2, write the equation of the transformed function g(x) after a vertical STRETCH by a factor of 3. g(x) = 3x² g(x) = (1/3)x² g(x) = (3x)² g(x)=x²-3

You notice that your 39 gallon aquarium is leaking 1.5 gallons of water per day. Write a function 'f(t)' to represent the amount of water in the aquarium as a function of time 't' in hours. Suppose the leak is repaired after 7 hours. Identify the restricted Domain and Range. Make sure you select 1 function and 1 Domain/Range option. Domain: [0,7] & Range: [28.5, 39] Domain: [0,26] & Range: [0,39] f(t)=39-1.5t f(t)=39+1.5t f(t)=1.5+39t Domain: [1.5,7] & Range: [0,7]

For f(x) = (x − 1)³ and g(x) = 1 - 8x, find the following. (a) (fog)(x) (b) (gof)(x) (c) f(f(x)) (d) f²(x) = (f. f)(x)

Select the correct answer. The area of undeveloped land in a suburban town is decreasing at a rate of 17.3% annually. In 2016, there were 3,400 acres of undeveloped land. If t represents the number of years since 2016, which equation can be used to determine after how many years the town will have 900 acres of undeveloped land remaining? A. 3,400 900(0.1.73)^t B.900=3,400(0.827)^t C. 900 = 3,400(1.173)^t D. 3,400 = 900(0.9827)^t

Write a general formula to describe the variation. The square of T varies directly with the cube of a and inversely with the square of d; T = 3 when a = 2 and d=6 T² = (Use integers or fractions for any numbers in the expression.)

What is the transformation of the function f(x) = 2^(x-4) compared to the parent function f (x) = 2^x ? Shifted right 4 units Shifted left 4 units Shifted up 4 units Shifted down 4 units

An object is dropped from 20 feet below the tip of the pinnacle atop a 920-ft tall building. The height h of the object after t seconds is given by the equation h=-161 +900. Find how many seconds pass before the object reaches the ground. seconds pass before the object reaches the ground.

Consider the polynomial function. f(x) = x² + 2x³ - 11x² - 5x - 6 Which statement correctly describes the number of possible positive zeros and the number of possible negative zeros? The number of positive zeros is either 2 or 0. The number of negative zeros is either 2 or 0. The number of positive zeros is either 2 or 0. The number of negative zeros is 1. The number of positive zeros is 1. The number of negative zeros is either 3 or 1. The number of positive zeros is either 3 or 1. The number of negative zeros is either 2 or 0.

What is the inflection point of the graph of f(x) = -x + 24x² - 27?

I am the only toolkit function that has a start and end number for the range. I am also the only that is cyclic, meaning I repeat over and over. Which toolkit function am I? Linear Function Quadratic Function Constant Linear Function Square Root Function Rational Function Absolute Value Function Cubic Function Logarithmic Function Sine Function Exponential Function

Let f (x) = (x + 1)³ and g(x) = f-¹ (x). What is the slope of the curve g(x) = f (x) at the point (8, 1)? g'(8) = -1 g'(8) = 1/12 g'(8)= - 1/12 g' (8) = 1

3 points: Suppose a children's swimming pool is filled with 34 gallons of water, but it has a small leak and loses 1.3 gallons of water per hour. a) Write a function, W(t), to represent the amount of water in the pool W (in gallons) as a function of time t (in hours). b) Suppose that the leak is repaired after 6 hours. Identify the restricted domain and range using any desired notation.

I am the only toolkit function whose domain contains no negative numbers but my range does. Which toolkit function am I? Exponential Function Logarithmic Function Absolute Value Function Quadratic Function Rational Function Square Root Function Linear Function Cubic Function Constant Linear Function Sine Function

Let f(x) be defined such that f(2) = 3 and f'(x) = cos(1/x² + x) where 1 < x < 4. Part A: Find the tangent line approximation for f(2.1). (25 points) Part B: If f(2.1) has an actual value of 2.12, use the shape of the graph to determine if this is an overestimate or underestimate. Justify your answer. (15 points)

Determine and classify the discontinuities, if any, of m. m(x) =6x/(7x-x^2) State the removable discontinuities, if any, of m. If multiple removable discontinuities exist, enter solutions using a comma-separated list. m has a removable discontinuity at x = m has no removable discontinuities. State the non-removable discontinuities, if any, of m. If multiple nonremovable discontinuities exist the solutions using a comma-separated list. m has a non-removable discontinuity at x = m has no nonremovable discontinuities.

A ball bounces to a height of 6.1 feet on the first bounce. Each subsequent bounce reaches a height that is 82% of the previous bounce. What is the height, in feet, of the fifth bounce? Round your answer to the thousandths place. 05.002 ft 02.758 ft 2.262 n 1.784 ft

f(x) = |x| g(x) = x + 1 We can think of g as a translated (shifted) version of f. Complete the description of the transformation. Use nonnegative numbers. To get the function g, shift f up/down/left/right ✓ by units.

While a function may not be one-to-one when defined over its "natural" domain, it may be possible to restrict the domain in such a way that it is one-to-one and the range of the function is unchanged. For the function f(x) = -x²-3, decide on a suitable restriction on the domain so that the function is one-to-one and the range is not changed. Determine a suitable restricted domain for f. Choose the correct answer below. OA. [-3,00) OB. [3,00) OC. [0,00) OD. [-3,3]

An employee at the bank notices an abandoned account with a balance of $360. The bank charges a monthly fee of $8 to maintain an account. The equation for this situation is y = 360 - 8x, where is the number of months, and y is the balance in dollars. Part A: Find the y-intercept. Show your work. Part B: Find the x-intercept. Show your work. Part C: Interpret the meaning of the x- and the y-intercept in terms of the problem.

In simplest form, what is the ratio of the change in y to the change in x for this relationship? Fill in the following: y increases units for every units of increase in x.

Given the functions ƒ(x) = 2x² − 3x + 4 and g(x) = −3x – 1 determine the value of (ƒ + g)(−1). 2 5 11 9

f(x) = 2x g(x)=x-3 What is the domain of f(x)/g(x) = 2x / x-3 ? A. the set of all real numbers B. the set of all real numbers greater than 0 OC. the set of all real numbers not equal to 0 D. the set of all real numbers greater than 3 E. the set of all real numbers not equal to 3