Let f be the linear function  f(x) = −2x + 6. (a) The rate of change of f is _____ . (b) The graph of f is a _____ (circle, parabola, polynomial, line), with slope ____ and y-intercept  ____.

Q: The reproduction function for a whale is estimated to be  f(p) = −0.0005p2 + 1.03p,  where p and…

A: The reproduction function for a whale  f(p) = −0.0005p2 + 1.03p   f'(p) = -0.001p+1.03   For maximum…

Q: Consider the linear function f(x) = - 4x + 3:(a) Find the slope and y-intercept.(b) What is the…

A: Given: fx=-4x+3 We know that for linear functionfx=mx+c, slope is m and y-intercept is c Similarly,…

Q: The graph shows the depth of water W in a reservoir over a'one-year period as a function of the…

A: Mark the coordinates at x = 150  and x = 300. From the graph, depth of water at x = 150 days is 175…

Q: The graph of a linear function f is given. y 2 X 1 (a) Find the rate of change of f. (b) Expressf in…

A:

Q: A function is given (either numerically, graphically, or algebraically). Find the net change and the…

A: Given function: g(x)=(x+1)2 To find: The net change and the average rate of change of the function…

Q: large pond is filled with a garden hose at the rate of 15 gal per minute Initially the pond contains…

A: Here we need to find volume function with respect to time.

Q: Weather balloons are filled with hydrogen and released at various sites to measure and transmit data…

A: We know that , the linear function can be written as :  f( x ) = a x + b  Where a is a slope and b…

Q: By noon, 3 inches of rain had fallen during a storm. Rain continued to fall at a rate of inch per…

A: We will find the amount of rainfall.

Q: The reproduction function for a whale is estimated to be  f(p) = −0.0005p2 + 1.06p,  where p and…

A: Consider the given function, fp=-0.0005p2+1.06p find the first derivative of the function with…

Q: What is the linearization of a function at a point . What is required of at for the linearization to…

A: Linearization is a process of finding linear approximation of a function at some point. This process…

Q: A local fruit company recently released a new flavor of applesauce. By the end of the first year,…

A:

Q: uppose a tour guide has a bus that holds a maximum of 110 people. Assume his profit (in dollars) for…

A:

Q: (a) Find an equation for the family of linear functions with slope 2 and sketch several members of…

A:

Q: Weather balloons are filled with hydrogen and released at various sites to measure and transmit data…

A:

Q: The graph of a linear function f is given. (a) Find the rate of change of f. (b) Express f in the…

A: Linear functions are functions with linear relationship between the dependent variable y and…

Q: The graph of a linear function f is shown. Identify the y-intercept and x-intercept. OA yintercept…

A: x intercept where function intersect with x axis and y intercept where function intersect with y…

Q: The water level in a glass decreases 0.4 cm each hour due to evaporation.  At the beginning of the…

A: The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the…

Q: A linear function is described either verbally, numerically, or graphically. Express f in the form…

A:

Q: Let x represent the number of years after 1970. Find a formula in slope intercept form for a linear…

A:

Q: Caren rides her bicycle along a straight road from home to school, starting at home at time t-0…

A: We are given that during the time interval 0≤t≤12 minutes, her velocity v(t), in miles per miles per…

Q: Weather balloons are filled with hydrogen and released at various sites to measure and transmit data…

A: Given that:  A weather balloon is filled with hydrogen at the rate of 0.5 ft3/s. Rate ( m) = 0.5 ft…

Q: Millage rate is the amount per $1000 that is often used to calculate property tax. For example, a…

A: (a) The fixed tax is $ 172 and the variable tax is 0.019x.

Q: using a graphing calculator or computer algebra system. Illustrate local linearity for f (x) = x 2…

A: Graph the function of f(x)=x2 by inputting the function in graphing utility and setting an…

Q: Linear Function: g0) = 4x-2 a. What is the domain of f0) and g(x) ? b. What is the înitial value of…

A: Given function is g(x)=4x-2

Q: 25. Appreciation A new house was sold for $1,183.000 siu years after it was built and purchased. The…

A:

Q: 1 Taren was modeling the rate of decay of a certain medication in the blood stream based on the…

A: Given function f(x) = 500 (0.25)x Here f(x) represents the amount of medicine, in grams, left in the…

Q: PROVE: Functions with Constant Rate of Change Are Linear Suppose that the function f has the same…

A: a). The average rate of change of is the ratio of change in output values and the change in input…

Q: . Let f be a function with constant rate of change. Then(a) f is a function and f is of the formf1x2…

A: (a) The highest degree of f is 1 because the rate of change of function f is constant.

Q: The sand in an hourglass drops at a constant rate of 2.5 cubic millimeters (mm3) every second.  The…

A: Given  The sand in an hourglass drops at a constant rate of 2.5 mm3 per second. Y is the amount of…

Q: 3.The population of birds in a region was measured to be 6300 birds in the year 2015, and 8700 birds…

A: 3. The population of birds in a region was measured to be 6300 birds in the year 2015,and 8700 birds…

Q: Let f be the linear function f(x) = -4x + 8. (a) The rate of change of f is (b) The graph of f is a…

A:

Q: A function is given (either numerically, graphically, or algebraically). Find the net change and the…

A: Given: f(x) = x2 - 2x To find the net change, Net change=f4-f1 Now we find f(4) as,…

Q: The reciprocal of every linear function has no x-intercepts.       True   False

A: Every linear function can be written in the form y=mx+c where m is slope and c is y-intercept. The…

Q: Let f(x)=x2+x−12f(x)=x2+x-12. Find the average rate of change in ff over the interval [0,3][0,3].…

A: The average rate of change of a function f(x) over an interval a,b is given by f(b)-f(a)b-a.

Q: Weather balloons are filled with hydrogen and released at various sites to measure and transmit data…

A: Since, Weather balloons are filled with hydrogen and released at various sites to measure and…

Q: A company is increasing production at the rate of 25 units per day. The daily demand inciting is…

A: Since, it is given that company production is increasing at the rate of 25 units per day.⇒dqdt=25…

Q: Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on…

A:

Q: World grain production was 1,241 million tons in 1975 and 2,048 million tons in 2005, and has been…

A:

Q: The water level in a glass decreases 0.4 cm each hour due to evaporation. At the beginning of the…

A: Part A Let y represent water level, x represent time and 0.4cm/hour is the rate of evaporation. So…

Q: Find the linearization of the function at x = a = -4

A: Since the function is not given so i have assumed the function as f(x)

Q: Amenda is hired by an accounting firm at a salary of $60,000 per year.Three years later her annual…

A: This question is based on finding equation of line.

Q: guide has a bus that holds a maximum of 84 people. Assume his profit (in dollars) for taking n…

A: Given: P(n)=n(42-0.5n)-84

Q: A large koi pond is filled from a garden hose at the rate of 18 gal/min. Initially, the pond…

A:

Q: A tractor has an initial price of $8000.00 and sells for $1100.00 after 23 years. Assume that the…

A: Tractor intital price at t = 0, Vo = $8000 After t = 23 years,  price V = $1100

Q: use linear functions. The linear depreciation method assumes that an item depreciates the same…

A: we have to graph the function d. To graph a linear function, determine two points of the graph…

Q: A large koi pond is filled from a garden hose at the rate of 18 gal/min. Initially, the pond…

A: It is given that the garden hose is filling with water at a rate of 18 gal/min. The initial volume…

Q: A local fruit company recently released a new flavor of applesauce. By the end of the first year,…

A: In the given question we have to express profit(P) as a function of time in years(x)

Q: The graph of a linear function f is given. y X 1 (a) Find the rate of change of f. (b) Express f in…

A: Equation of line ,  y - y1 = m ( x - x1 )  Here ( x1 , y 1 ) is a point and m is the slope of line…

Q: A roof has a 0.3-inch layer of ice on it from a previous storm. Another ice storm begins to deposit…

A: Given. A roof has a 0.3 inch layer of ice on it from a previous storm. Another ice storm begins to…

Q: In a study on the speed of muscle contraction in a certain species of frogs under various loads,…

A: To find that the number to which v(x) approaches as x increases