Examples
1) If y= 9 for every value of x, can y be regarded as a function of x ? Yes
2) A factory produces firebricks. For every cubic metre of clay, it produces 1000 fire bricks of which 5% may be rejected because of low quality. Assume x, the amount of clay in cubic metres and y, the number marketable bricks produced. Formulate a function of y dependent on x, Find its domain and range. y= 1000x - 50x= 950x.
3) Given f(x)= x²- 2x +1, determine f(-3) and f(3). 16?4
4) The relationship between the price, p, and the quantity demanded, Q, for a particular commodity is given by Q= f(P), Assuming f(P)= 12- 3p, find the quantity demanded at various prices, and determine the domain, and the range of Q= f(P). (0,4), (0,12)
5) For the function f(x)= 3x³-9, determine the value of the dependent value f(x) when the independent variable x equals to 2. 15
6) A firm sells eggs for Rs 6 a dozen for orders under 12 dozens and for Rs 5.50 a dozen for orders of atleast 12 dozens, In addition, it allows a rebate of Rs 15 to customer purchasing atleast 600 eggs. Express the farm's receipt R(x) as a result function of dozens of eggs x sold. Also, find the domain of R(x).
7) Sketch the graph of the function y= 3x +3.
8) Plot the graph of y= 2.
9) Plot the graph of absolute value function f(x)= |x|.
10) Draw the graph of the function y= x²/x.
11) Show that f(x)= (x²-2x +3)/(x²- x -20) is undefined for x= 5 and x= -4.
12) Test weather the following function are even or odd.
a) g(x)= x(x -1). Neither even nor odd
b) f(x)= x + 1/x. Odd
c) h(x)= 4x⅖+1. Even
13) Find x and y intercepts for the function, y= bx/a + c.
14) A manufacturer earns Rs4500 in the first manth and Rs 6000 in the second month. On plotting these points, the manufacturer observes , a linear function may fit the data.
a) Find the linear function that fits the data. y= 1500x + 3000
b) make a prediction of earning for the third month. 7500
15) The life expectancy , E, of males in 1980 in a country was 70 years, in 2000 it was 75 years.
a) Express E as a linear function of time, t. E= 0.25t +70
b) Using the equation i) make a prediction of life expectancy of males in 2008. 77
16) Find the slope of each of the lines through the points
a) (2,3) and (5,9). 2
b) (1,4) and (2,-3). -7
c) ( 1,5) and (4,5). 0
d) (7,5) and (7,9). Undefined
17) Find the slope of the function 3y - 6x + 15= 0. 2
18) The following table shows the quantity sold x of an item produced by a manufacturer and the total revenue earned thereby. Express the total revenue R as a linear function of the quantity sold x that satisfies the given data:
Quantity sold(x): 1. 2
Total revenue: 7 10
19) Find the average of the rate of the change of the functions y= 3x -4 over the interval [1,5]. 3
20) Following is a cost versus time graph for the local telephone calls :
Using the above information find the average rate of change in telephone costs with respect to minutes for
a) 3 minutes . Ra 0 per minute
b) the second 3 minutes of a 6 minutes call. Rs 0.20 per minute.
21) Market price for a pot of ink is fixed to be Rs 2. Find the marginal revenue if the revenue be R per ink sold. Assume the revenue function to be linear. Make graphical representation of marginal revenue.
22) Following data are collected after survey by a soft drink manufacturing company.
No of bottles sold(x) price (y)
20000 1.00
15000 1.50
10000 2.00
5000 2.50
Find the functional relationship that exists between x and y. y= -10000x + 30000
23) A machine costing Rs 10000 has probable life of 10 years. The estimated scrap value at the end of is 1000, using the straight line method of depreciation find the annual depreciation and construct the depreciation function. D(t)= -900t+ 10000, 900
24) Suppose Ram borrows Rs 5000 at a simple interest rate 8% per year
a) Find a formula for the amount A that Ram will own in r years. 8200
b) Find the amount Ram will owe in 54 months. 6800
25) The overhead expenditure in a workshop is Rs 150 and the cost for each piece manufactured is Rs 10. Construct cost function C(x). What is the domain and the range of C(x)? {150,160,.....}
26) A company sells x tins of talcum powder each day at Rs 10 a tin. The cost of manufacturing and selling these tins is Rs 7 per tin plus a fixed daily overhead cost of Rs 600. Determine the profit function. What is the profit if 500 tins are manufactured and sold a day ? How do you interpret the situation if the company manufactures and sells 100 tins a day ?
27) Without drawing the graph, determine the vertex for each of the parabolas;
a) y= 8x². (0,0)
b) y= -x²+ 8x -16. (4,0)
28) Graph the function f(x)= 3x²+ x -4. Find its vertex and the y-intercept , if they exist.
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Find the domain in the range of the each of the following functions given the functions find given the functions during the functions find suppose the company manufacturing toys and reflection of depend the number of Taj manufacture there is also a fixed establishment cost 500 determine whether the following function are even or odd which of the following person increasing decreasing neither increasing now decreasing find X and Y intercept the following functions the salary of an employee in the year 1983 wash 12995 device 1350 Express salary as a linear function of time estimated is salary for the year 2000 20% of the population of educated in 1936 820 note the percentage of the population number of your since 1950 Express is a linear function using the function relation in the year find the slover the line passing through the point 3568 2437 final slope of the function fallen table gives the result quality control test of the horizontal Lance in the manufacturing concern number of Reliance produced number of land defective Express as a function of the total size of the particular Bond for a fan during the month of April was 5000 the end of the September 5 months period the total annual profit rupees for a toy manufacturing company for the manufacturer in the cells numbers toys is given by how many tall the company muscle for here to achi maximum profit what is the profit by tie on the maximum acid a government manufacturer is planning to produce a new varieties of servers it in birds 1.5 lakh and a variable cost 150 find the cost function revenue function profit function aise mere paise is planning production ko new varieties of soap for the first year the pH cost for the setting of the new production lines are 1.25 lakh variable cost producing is pair of since 35 the cells department project 1500 years can be sold in the first year at the rate of 160 AP determine the cost function for the total cost producing determine the revenue function for the total function for the profit from the cell of experience Italy construction units manufacture products 3.5 X 125 unit is sold for 6 determinant number of unit that should be produced in sold to insert no loss if the selling price is increased by half of a rupees per unit what would be the break even point 6000 delivered price for unit 4 recharge to guarantee know lost and textbook publisher find the production that up the office cost 10000 it is book can be sold 30th reminder the products cost associated with 5 and the fixed cost or 7 produced can be solved 7 find the break even point a company manufacturer is to watch is for rupees 1500 / 17 the unit price 38400 and a variable cost 420 for watch at what level production a distributed wapas us 5000 model in the stores that wishes to distribute in a month for experience it is known that the demanding the number of totals per month is a function of the price 2017 television manufacturing determine that the total cost for X number of sales given by 5000 states of the 6 determine the breakup in point are respected with the total cost function revenue functions for a company that produces saxious particular produced find the break even values the values of that profit the values are result in the laws are many years will be taken investment 1000 itself Sunita has a 1000 deposit Bank of or 6% compound annually another one offers 5% choose if you want maximum returns after 3 years
