1 Given the following ly = x - 4. a) Graph both equations on the same coordinate grid. b) Describe what is meant by a solution to a system of equations. -10 -5 Solving the system means finding all solutions with formulas involving some number of parameters c) How many solutions does this system have? d) What is/are the solution(s) to this system? x=2, y=-2 (2,-2) x=5, y=1 (5,1) 2 Using the system of equations in #1, state the size of the window you would need on your calculator to capture the solution(s). x min = y min = x max = y max =For Questions 7 and 8, find the LCM of each set of polynomials. 7. 5p - 20, 15p - 60 A 75(p -4) B 15(p - 4) Cp -4 D 5(p - 4) 8. t2 - 8t + 15, t2 - t - 20 F (t + 3)(t - 5)(t + 4) H (t+ 3)(t - 5)(t - 4) G (t -3) (t + 5)(t -4) J (t -3) (t -5)(t + 4) 9. Determine the equations of any vertical asymptotes of the graph of /(x) = xz + 5x+6 x - 1 A x =1 B x =-2 C x = -2, x =-3 D f(x) = 1 10. Determine the values of x for any points of discontinuity in the graph of f(x) x-+6x+5 x+5 F x =5 H x =-5 G x =1 J x =-1, x= -5 11. Which rational function is graphed? A f(x) = 3 Cf(X) = x+2 3 21 B A(x) D f(X)= x - 2 x - 22 Determine which pair of functions are inverse functions. A frfx)=ox B f{x}=Bxl [I):%I '9in :I+'I[i H 2 1 1' Find the area of a circle whose radius is 3.:r5;-,!E.s2 feet. Use 3.14 for It. 9 The time T in seconds that it takes a pendulum to make a complete swing back: and forth is given lav the formula T = BEE Where a" is the length ofthe pendulum in feet and g is the acceleration due to gravitv, 32 feet per second squared. In Tokyo, Japan, a huge pendulum in the Shinjuku building measures ?3 feet 9.?5 inches. How long does it take for the pendulum to make a complete swing? 15 State the number of real zeros for the function whose graph is shown here. 16 Write the expression 9n + 7n3 - 6 in quadratic form, if possible. 27 The value of a certain car depreciates according to v(t) = 28500e-0.1860 where t is the number of years after the car is purchased new. a. What will the car be worth in 18 months? b. When will the car be worth half of its original value? c. When will the car be worth less than $1000? 20 Which function represents exponential decay? X A y = 20 By = 16(1.4)* C y = 20 D y = 8x334 The volume of gas v varies inversely as the pressure p and directly as the temperature t. a) Write an equation to represent the volume of a gas in terms of pressure and temperature. Is your equation a direct, joint, inverse, or combined variation? b) A certain gas has a volume of 8 liters, a temperature of 275 Kelvin, and a pressure of 1.25 atmospheres. If the gas is compressed to a volume of 6 liters and is heated to 300 Kelvin, what will the new pressure be? c) If the volume stays the same, but the pressure drops by half, then what must have happened to the temperature