IMPORTANT NOTES HERE IS AN EXAMPLE OF A SCANTRON FORM FOR YOUR EXAM.

Transcription

1 IMPORTANT NOTES HERE IS AN EXAMPLE OF A SCANTRON FORM FOR YOUR EXAM. YOU NEED TO MAKE SURE YOU PROPERLY FILL OUT THE SCANTRON FORM.. Write and bubble in your first and last name.. VERY important, write and bubble in your ASU affiliate id in the Identification # field.. Write and bubble in the SLN of your course in the Special Codes field.

2 MAT7 Review Problems for Eam Equation represents a function. Determine whether the following equations define y as a function of. a. y 5 b. y + 7. Determine whether the following equations define y as a function of z. 4 a. y 4z b. y z 5 Find the value of the function. If a rock falls from a height of meters on Earth the height H (in meters) after seconds is approimately. H ( ) 4.9 What is the height after seconds? d 4. The function P ( d) + gives the pressure, in atmospheres (atm), at a depth d feet in the sea. Find the depth when the pressure is (atm). Domain of function 5. Find the domain of the following function: 6. Find the domain of the following function: Find the domain of the following function: 6 8. Find the domain of the following function: Difference quotient 9. Find and simplify the difference quotient,. Find and simplify the difference quotient, f ( + h) h, h for the function f ( + h) h, h for the function + Combining functions. A firm is considering a new product. The accounting department estimates that the total cost, C(), of producing units will be C() The sales department estimates the revenue, R(), from selling units will be R() 85, but no more than 6 units can be sold at that price. Find and interpret (R C)(6).

3 . A firm is considering a new product. The accounting department estimates that the total cost, C(), of producing units will be C() The sales department estimates the revenue, R(), from selling units will be R() 75, but no more than 55 units can be sold at that price. Find and interpret (R C)(55). Obtaining information from graphs. Given the graph of y f () a. For what value(s) of b. For what value(s) of 4. Given the graph of y f () a. Find the range of y f () b. Find the domain of y f () Suppose, is the point (, ) on the graph of f()? 6. Suppose 4+ 5 is the point (,) on the graph of f()? Even/Odd 7. Perform the algebraic tests for even and odd to determine if the function is even, odd or neither. 8. Perform the algebraic tests for even and odd to determine if the function is even, odd or neither.

4 Increasing/Decreasing/Constant and Local Min/Ma 9. Using your calculator graph the function + a. Determine the open interval for which the function is increasing or decreasing. b. What are the local maimum and local minimum? 4. Using your calculator graph the function a. Determine the open interval for which the function is increasing or decreasing. b. What local maimum and local minimum?. The height s of a ball (in feet) thrown with an initial velocity of 8feet per second from an initial height of 6 feet is given as a function of the time t (in seconds) by s( t) 6t + 8t+ 6 a. Determine the time at which the height is maimized. b. What is the maimum height?. The profit P in dollars generated by selling units of a certain commodity is given by P( ) 5+.4 a. How many units must be sold in order to maimize profits. b. What is the maimum profit? Average rate of change. Find the average rate of change for 4. Find the average rate of change for + from to. f ( ) 4 + from to. Piecewise defined function 5. Write the definition (formula) for the function f(). 6. Write the definition (formula) for the function f(). 7. Evaluate the piecewise function at the given value of the independent variable. 4 if + 7 if >, at a.) and b.)

5 8. Evaluate the piecewise function at the given value of the independent variable. if + 7 if >, at a.) and b.) Transformations 9. Starting with the base function. Starting with the base function y, describe in words the transformed function y, describe in words the transformed function ( ) ( + 4) +. The following graph of g() g(). is the transformation of the graph of. Find an equation (formula) for. The following graph of g() g(). is the transformation of the graph of. Find an equation (formula) for Linear functions and their applications. The price p and the quantity sold of a certain product obey the demand equation: p + 5 What is the revenue when units are sold? 4. The price p and the quantity sold of a certain product obey the demand equation: p + What is 5 the revenue when 5 units are sold? 5. Identify the slope (m) and the y-intercept (b) for the linear function 6y 7 6. Identify the slope (m) and the y-intercept (b) for the linear function y The revenue for a firm is given by R( ) 8 and the cost is given by C( ) , where is the number of units produced and sold. Find the break-even point for the firm. 8. The revenue for a firm is given by R( ) and the cost is given by C( ) 9+, where is the number of units produced and sold. Find the break-even point for the firm.

6 9. The data listed in the following table represents the appearance temperature vs. the relative humidity in a room. Relative Humidity (%) Apparent Temperature y a. Use your calculator to find (linear regression) the line of best fit to the data b. Using the regression in part (a) approimate the room temperature when the relative Humidity is 8%. 4. The aver life epectancy in the United States has been rising steadily over the past few decades, as shown in the table below. Year (after 9) Life Epectancy a. Use your calculator to find (linear regression) the line of best fit to the data b. Using the regression in part (a) approimate the life epectancy in the year 995.

7 MAT 7 Test Review Answers Note: There is a reasonable assumption that most of these answers are not incorrect.. a. No b. Yes. a. t.5 seconds b. s 6 feet. a. Yes b. No. a. 5 units b. $88,5..4 meters feet (, ) (,) (, ) if 5. + if < 6. (, 5) ( 5, ) (, ) if 6. if < 7. (, ] 7. a. b. 8. [ 5, ) 8. a. b. 9. shift right by units; shift up unit 9. ( + h). h. shift left 4 units; shift down units. $85 means profit, income eceeds cost. g ( ) + +. $85 means loss, cost eceeds income. g( ). a. and b.,. $5, 4. a. [, ] b. [, ] 4. $6,5 5. No 5. m ; b Yes 5 6. m ; b 7. odd even 8., 9. a. decreasing (, ); increasing (, ) (, ) 7 b. local maimum ; local minimum. a. decreasing (, ) (, ) increasing (, ) (, ) b. local maimum ; local minimum 4 9. a. y ; b a. y ; b. 76.7