Math Chapters 1 and 2 review

Transcription

1 Math Chapters 1 and 2 review Name Solve the problem. 1) A person puts some warm turke leftovers in the refrigerator. Let T represent the temperature of the turke at M minutes after putting the turke in the refrigerator. Sketch a qualitative graph that describes the relationship between M and T. Complete the three ordered pair solutions of the linear equation and graph. 2) = 0 (-3, ), (0, ), (3, ) Find the slope of the line passing through the two given points. 3) (3.8, -3.1) and (6., 3) 1

2 Sketch the graph of the equation. 4) = ) = ) = Using the indicated slopes of lines L1 and L2, determine whether the lines are parallel, perpendicular, or neither. Assume that the lines are not the same. 7) m1 = 2, m 2 = 2 Determine the slope and the -intercept for the linear equation. 8) = 0 2

3 Determine the slope and the -intercept for the linear equation. Use the slope and the -intercept to sketch the graph of the equation. 9) = ) = Find an equation of the line that has the given slope and contains the given point. 11) m = 6, (, 3) 7 12) m = 0, (3, 2) 13) m is undefined, (-4, -7) Find an equation of the line passing through the two given points. 14) (3, -8) and (-7, -1) 3

4 Find an equation of the line that contains the given point and is parallel to the given line. 1) 9 + = 4, (3, ) 16) = 3, (4, 8) Find an equation of the line that contains the given point and is perpendicular to the given line. 17) = 1 + 9, (4, ) 7 18) = 10, (8, 7) Find an equation for the line. 19)

5 Solve the problem. 20) Some values for a relation are given in the table. Is the relation a function? Eplain A) Yes B) No Determine whether the graph is the graph of a function. Eplain. 21) Determine whether the relation is a function. 22) = 8 + 7( - 1) 23) 9-3 = 27 24) = 2

6 Solve the problem. 2) A computer science major found that the grade he earned on his programs increased with the time he spent working on them in the computer lab. He made a table of the hours spent in the lab and the corresponding program grades. Let g represent the grade earned when h hours are spent in the lab. Hours spentprogram Grade in lab a) Sketch a scattergram for the data. b) Sketch a line that comes close to the data points in the scattergram. Use our linear model to estimate the Program grade when 4 hours are spent in the lab. State whether ou used interpolation or etrapolation to obtain our result. 26) The number of people who have committed violent crimes (per 100,000 people) in the U.S. during various ears are listed in the table below. Number of Violent Crime Offenders Year (per 100,000 people) (Source: The American Almanac) Let f(t) represent the number of people who have committed violent crimes (per 100,000 people) in the U.S. in the ear that is t ears since Find a formula for f. Find the -intercept and interpret within the contet of the problem. Comments? 6

7 Solve the resulting equation for. 27) = 18 for = 7 Evaluate the function at the given value of. 28) f() = -6-3, f(4) 29) f() = 4 +, g(a + 1) For the given function, find the value of that corresponds to the given value of f(). 30) f() = 4-2, f() = A graph of the function f is sketched in the figure below. Use the graph to find the indicated values ) Find f(-2) 32) Find when f() = -3 Find the -intercept and -intercept of the function. 33) f() = 2-8 7

8 Solve the equation. 34) 6 - (3-1) = 2 Solve the problem. 3) Sprint charges a flat monthl fee of $16.89 to use their services. You also must pa $0.10 per minute of talking on the telephone. Let f(t) represent the monthl phone bill (in dollars) from talking on the phone for t minutes. i) Find an equation for f. ii) What is the slope of f? What does it mean in terms of the situation? 36) The following data represents the Olmpic winning time in Women's 100 m Freestle. ear winning time a) Let f(t) represent the winning time in the Women's 100 m Freestle at t ears since Perform the first three steps of the four-step modeling process to find an equation for f. b) Find the slope of f. What does it represent in this situation? 8

9 Answer Ke Testname: REVIEW-CH1-2 1) T M 2) (-3, 4), (0, 0), (3, -4) ) ) - - 9

10 Answer Ke Testname: REVIEW-CH1-2 ) - - 6) - - 7) neither 8) m = 1, -intercept: (0, 11) 12 9) m = 1, -intercept: (0, 3)

11 Answer Ke Testname: REVIEW-CH1-2 10) m = 0, -intecept: (0, 4) ) = ) = 2 13) = -4 14) = ) = ) = 4 17) = ) = 7 19) = ) B 21) not a function 22) not a function 23) function 24) not a function 11

12 Answer Ke Testname: REVIEW-CH1-2 2) a) b) The Program grade should be about 8. Answers ma var slightl. Interpolation was used to obtain the result. 26) f(t) = 18.89t ; Answers ma var. 27) 3 28) ) 4a ) ) -2 32) -4 33) -intercept: (4, 0) -intercept: (0, -8) 34) 1 3 3) i) f(t) = 0.10t ii) 0.10; The charge per minute is $ ) a) f(t) = Answers ma var. b) The slope is about which means that the winning time is decreasing b of a second each ear. 12