Functions Questions and Answers

The size of a stray cat population at the bay area of a certain city grows at a rate of 8% monthly. If there are 350 stray cats currently, find how many stray cats should be expected in 24 months. Use P(t)= 350e0.08t, and let t be 24 months. (Round your answer to the nearest whole number.)

Identify the independent and dependent variables for the given linear situation. Write an equation that represents the linear relationship between the variables. Use the equation to answer the question. Be prepared to show how you used the function equation to answer the question. Situation: There is a linear relationship between the price a shop charges for a product and the quantity of that product that will sell at that price. If the shop charges $6 for a t-shirt, they will sell 27 of them that week. If the shop charges $14 for a t-shirt, they will sell only 3 of them that week. Question: How much did the shop charge for a t-shirt if they sold 45 t-shirts in one week? Round final answers to the nearest cent if rounding is necessary. Answer: They charged $

Sal is running on a treadmill at the gym. He is going to run for 7 miles at a constant speed of 1 mile per 8 minutes. Graph the distance Sal will run as a function of time. y= 1/8 x+0

Find the end behavior of the following polynomial: f(x)=-7(x-11)^3(x+13)³(x+2)(x-3)5 As x → ∞, f(x)→→ -∞ As x→ -∞, f(x) → ∞ As x→∞, f(x)→∞ As x→ -∞, f(x) → ∞ As x→ -∞, f(x) → -∞ As x→→ -∞, f(x)→ -∞ As x→ ∞, f(x) → ∞ As x→ -∞, f(x) → -∞

Which of the following describes the zeroes of the graph of f(x) = 3x6 + 30x5 + 75x4? -5 with multiplicity 2 and 1/3 with multiplicity 4 5 with multiplicity 2 and 1/3 with multiplicity 4 -5 with multiplicity 2 and 0 with multiplicity 4 5 with multiplicity 2 and 0 with multiplicity 4

The monthly rent for a pizza parlor is $1,200. The average production cost per pizza is $6.75. The monthly expenses for the pizza parlor are given by the function E(x) = 1,200 +6.75x, where x is the number of pizzas sold. For x pizzas sold, the pizza parlor's revenue is given by the function R(x) = 12.5x The monthly profit of the pizza parlor is the difference between its revenue and its expenses. Which function represents the monthly profit, P(x) ? A. P(x) =5.75x + 1,200 B. P(x) = 1,200 + 19.25x C. P(x) = 6.25x - 1,200 D. P(x) = 5.75x - 1,200

Betty has a checking account and a non-interest-bearing savings account. Function Crepresents her checking account balance, where x is the number of months. Function S represents her saving account balance. C(x) = -|240x -140| + 1,400 S(x) = 450x + 100 Which function represents Betty's total account balance, T(x)? A. T(x) = -|240x - 140| + 450x + 1,500 B. T(x) = -|240x - 140| + 450x + 1,400 C. T(x) = |240x + 140| +450x + 1,500 D. T(x) = -|240x - 140| +450x + 1,300

The following equations define x = = f(t) and y = g(t) implicitly as functions of t. x³ - 2²2² = -17, 5y³ + 3t² = 67, Find the slope of this curve at the point on the curve associated with t = 3. Slope = Σ

There is a formula that estimates how much your puppy will weigh when it reaches adulthood. The method we present applies to medium-sized breeds. First find your puppy's weight w at an age of a weeks, where a is 16 weeks or less. Then the predicted adult weight W = W(a, w), in pounds, is given by the formula W = 52w/a In this exercise we consider puppies that weigh w = 2 pounds at age a. (a) Write a formula for W as a function of the age a. W =

x = -5 : Determine if the relation is a function. If it is not, identify two ordered pairs as proof.

A certain species of deer is to be introduced into a forest, and wildlife experts estimate the population grow to P(t) = (976)3 t4. where t represents the number of years from the time of introduction. Step 2 of 2: How long will it take for the population to reach 26352 deer, according to this model?

Two ant colonies are growing at the exact same rate. The first colony, however, has a larger population than the second colony. The equation f(t) = 300 (1.03)t models the population of the first colony over time. What equation models the second colony g(t) if g is 85% the size of f?

Given that 3 - 2i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x) = x4 - 9x³ - 9x² + 201x - 520

Consider the polynomial below. x3 + x2 - 14x - 22 Use the remainder theorem to determine which binomial expression divides the polynomial so that the remainder is 2. A. x-2 B. x-1 C. x + 3 D. x + 4

A graphing calculator is recommended. A function is given. f(x) = 9+ x + x² - x³ (a) Find the local maximum and minimum values of the function and the value of x at which each occurs. State each answer rounded to two decimal places. (b) Find the intervals on which the function is increasing and on which the function is decreasing. State each answer rounded to two decimal places.

Which of the following describes the zeros and end behavior when the function is graphed? A. zeros: x= -6,x= -1,and x = 1; As x decreases in value, f(x) increases in value. Ax increases in value, f(x) increases in value. B. zeros: x= -6,x= -1,and x = 1; As x decreases in value, f(x) decreases in value. As x increases in value, f(x) increases in value. C. zeros: x= -6and x = 1; As x decreases in value, f(x) decreases in value. As x increases in value, f(x) increases in value. D. zeros: x= -6and x = 1; As x decreases in value, f(x) increases in value. As x increases in value, f(x) increases in value.

Two variables appear to have an exponential relationship. What pattern(s) does the scatterplot suggest for the model? Select the two correct answers. It is only increasing or only decreasing. It has a point of inflection. It is only concave up or only concave down. It has one or more extrema. It is both concave up and concave down.

Given: (x is number of items) Demand function: d(x) = 440-0.5x² Supply function: s(x) = 0.6x² Find the equilibrium quantity: Find the consumers surplus at the equilibrium quantity:

f(x)=x-1. Find the inverse of f(x). A. f^-1(x) = 1-x B. f^-1(x) = x C. f^-1(x) = x + 1 D. f^-1(x) = x −1

2. Use A = Pe^rt to solve the following problem. A sum of $14,000 is invested at an interest rate of 6.85% per year. Find the amount in the account after 10 years if the interest is compounded continuously.

For the function f(x) = 3x+5/x+5, find f-¹(x).

Assume that the function f is a one-to-one function. (a) If ƒ(7) = 9, find ƒ−¹(9). Your answer is (b) If ƒ−¹( − 2) = – 8, find ƒ( − 8). Your answer is

A homeowner with gas heat in her home has been reviewing her monthly gas bills from the last several years. She has noticed that her highest gas bill is for January, when she owes x dollars. Then, the amount of she owes each month decreases to its smallest size, y dollars, for July. The amount of her gas bill slowly increases back to its maximum amount, x dollars, for the following January. This pattern has continued for all of the years of bills reviewed. Which of the following function types would best model the situation above? A. cube root B. trigonometric C. step D. exponential

You work as a cashier for a grocery store and earn $5 per hour. You also mow lawns and earn $10 per hour. You want to earn at least $50 per week, but would like to work no more than 10 hours per week. Which system of inequalities, along with y 20 and x20, would you use to solve the real-world problem?

Find the GCF of the given list. x16y5, xy5, x7y8

State the domain and range for the following relation. Then determine whether the relation represents a function. {(3, 1), (4,-1), (5, 1), (6,-1)} The domain of the relation is. (Use a comma to separate answers as needed.) The range of the relation is. (Use a comma to separate answers as needed.) Does the relation represent a function? Choose the correct answer below. A. The relation is a function because there are no ordered pairs with the same first element and different second elements. B. The relation is a function because there are no ordered pairs with the same second element and different first elements. C. The relation is not a function because there are ordered pairs with 1 as the second element and different first elements. D. The relation is not a function because there are ordered pairs with 3 as the first element and different second elements.

A company estimates that the marginal cost (in dollars per item) of producing x items is C'(x) = 1.7 -0.008x. If the cost of producing one item is $754, find the cost of producing 154 items. (Round your answer to the nearest cent.)

Graph the function f(x) = 7(x + 2)² - 6. Plot the vertex. Then plot another point on the parabola. If you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

Given that f(x)=x²-19 and g(x) = 6x +1, find (fg)(-1/6) A. (fg)(-1/6)= (Simplify your answer.) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. B. The value for (fg)(-1/6) does not exist.

State if the given functions are inverses. * g(x)=2x+4 f(x) = x-4/2 A) Yes B) No

Fill in the missing words for the following statement about functions: A function is a relationship between two sets of data, the input and output sets. and the set of outputs is called the___The set of inputs is called the___

The population P(t) of a culture of the bacterium Pseudomonas aeruginosa is given by P(t)=-1687t2 +83,000t+10,000, where it is the time in hours since the culture was started. (a) Determine the time at which the population is at a maximum. Round to the nearest hour.

For a given input value n, the function g outputs a value m to satisfy the following equation. 3m - 5n = 11 Write a formula for g(n) in terms of n. g(n) =

For the polynomial below, -3 is a zero. h(x) = x³ + x² − 9x-9 Express h (x) as a product of linear factors. h(x) =

For q (x) =-2x² +5x-5/x² +2 (a) Identify the horizontal asymptotes (if any). (b) If the graph of the function has a horizontal asymptote, determine the point (if any) where the graph crosses the horizontal asymptote(s). Separate multiple equations of asymptotes with commas as necessary. Select "None" if applicable. The graph has no horizontal asymptotes. The graph has at least one horizontal asymptote. Equation(s) of the horizontal asymptote(s): y = Crossover point(s):

In 2004, the population of a district was 26,400. With a continuous annual growth rate of approximately 5%, what will the population be in 2024 according to the exponential growth function? Round the answer to the nearest whole number.

Consider the given function f(x) = -3(x+1)² +12. (a) Determine whether the graph of the parabola opens upward or downward. (b) Identify the vertex. (c) Determine the x-intercept(s). (d) Determine the y-intercept(s). (e) Sketch the function. (f) Determine the axis of symmetry. (g) Determine the minimum or maximum value of the function. (h) Write the domain and range in interval notation. Write your answers in exact form.

The number of bats in a colony is growing exponentially. After 2 years, there were 207 bats. After 4 years, there were 1863 bats. If the colony continues to grow at the same rate, how many bats are expected to be in the colony after 11 years? Do not include units in your answer.

Find the function that is finally graphed after the following transformations are applied to the graph of y=√x in the order listed. (1) Vertical stretch by a factor of 2 (2) Shift down 3 units (3) Shift right 1 unit

Describing the Effect of the y-Intercept When comparing functions, such as Seth's scenarios for travelling to school, will the function with the greatest initial value continue to be the greatest as time increases? Explain why.

Find the domain of the function f(x) = In (x-3) + log (x - 5). (Give your answer as an interval in the form (*, *). Use the symbol co for infinity, U for combining intervals, and an appropriate type of parenthesis "(".")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.)

The number of people afflicted with the common cold in teh winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were afflicted. Find the following: A- Find the linear function that models the number of people inflicted with the common cold, C, as a function of the year, t. B- Find a reasonable domain and range for the function C. C- If the function C is graphed, find and interpret the x- and y-intercepts. D- When will the output reach 0? E- In what year will the number of people be 9,700?

For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain. f (x) = 2x+5 / 5x-2; g(x) = 8x/5x-2

Write in simplified form and list all restrictions on the domain. f(y) = 7+ y/y+6 - 6/ y^2-36 f(y)= (Simplify your answer.)

a. If x is increased from 2 to 3, how much does 1 + x/2 + x change by? change = b. Does the function increase or decrease when x goes from 2 to 3? The function ?

Suppose that the functions and s are defined for all real numbers x as follows. r(x)=3x-5 s(x) = 6x Write the expressions for (r-s) (x) and (r+s) (x) and evaluate (r.s) (2). (r-s)(x) = (r+s)(x) = (r.s) (2) =

Let y = (x+sin(x))⁴. Find g(x) and f(x) so that y = (fog)(x), and compute the derivative using the Chain Rule. f(x) = g(x) = (fog)' =

Juli is going to launch a model rocket in her back yard. When she launches the rocket, the function h(t) = -16r2 +681 model the height, h, in feet of the rocket above the ground as a function of time, t, measured in seconds. (a) When will the rocket hit the ground? (b) When will the rocket be 42 feet above the ground?

For f(x)=x+4 and g(x) = 4x+4, find the following functions. a. (fog)(x); b. (gof)(x); a. (fog)(1); d. (gof)(1)

Find the relative maxima and relative minima, if any, of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = 2x² + 864/x + 8 Relative maximum value(s): Relative minimum value(s):