Show Work on 16-20. No work needed for 1-15. all need to be answered using any calculations to get right solution.

18. Describe the steps you would take in order to solve the following logarithmic equation: log2 (x - 3) + log2 (x) = 2. Be sure to Include each step, any properties or rules that you use, whether or not there are extraneous variables, and the final solution. If there is an extraneous variable, discuss what makes it extraneous. BIUS Normal X2 X2 fx Enter your response here alwarebytesO logs 11. Solve for x: log (x + 10) = 3 x=64 x-54 O X-22 O X-2 12. The number of bacteria N on a rotten piece of food is given by the formula: N = 120ekt. If the number of bacteria N is NV = 480 whent = 3 (in hours), estimate the time required for the population of bacteria to triple in size. Round each step to the nearest thousandths. O t ~5.4 hours O t ~4.7 hours O t ~3.9 hours O t ~6.2 hours alwarebytes5kVt7ZiNY9n44jcB5 6. Find the resultant force acting on this box. 4 POINTS 3 N 20 N 6 N 18 N due southeast O 21 N due southeast O 11 N due southeast O 29 N due southeast 7. The work done by gravity as a projectile falls is . 4 POINTS Positive because the displacement and force vectors are parallel and in the same direction Negative because the displacement and force vectors are parallel and in opposite direction Zero Negative because the displacement and force vectors both point downwardsOf(2) = -3(x - 2)?(x + 1)2 Of(x) = -3(x+2) (2 -1) 7. Determine all intercepts and asymptotes of the rational function: 4 P f(a) = 4(x-2)(2+1) (+2)(2-1) Vertical asymptote: x=4, x=-2, x=1 O Horizontal asymptote: y=4 Y-intercept: (0, -4) X-intercepts: (-2,0), (1, 0) Vertical asymptote: x=-2 and x=1 O Horizontal asymptote: y=4 Y-intercept: (0, 4) X-intercepts: (2, 0), (-1, 0) Vertical asymptote: x=-2 and x=1 O Horizontal asymptote: none Y-intercept: (0, 4) X-intercepts: (2, 0), (-1, 0) Vertical asymptote: x=2 and x=-1 O Horizontal asymptote: y=4 Y-intercept: (4, 0) X-intercepts: (0, 2), (0, -1) lalwarebytes01 3 O 3. A ball is thrown up in the air from a height of 160 feet at a speed of 48 feet per second. Use the standard equation for projectiles h (t) = -16t2 + vot + ho to model the height of the ball overtime and find when it will reach the ground. 2 seconds O 5 seconds O 8 seconds 10 seconds 4. Identify the lead term, degree, and leading coefficient of the following polynomial function and describe the end behavior: f (x) = -3+723 -4x + Lead term: - 4x alwarebytes19. Explain In great detail how to build the unit circle and how to use it to find trigonometric function values. BIUS Normal E X2 X2 Enter your response here lalwarebytes13. Solve the triangle A 12 b B 8 A=33.69%, B=56.31', b=4v/5 A=41.81, B=48.19, b= 4v/5 A=56.31, B=33.69', b=V80 A=48.190, B=41.81, b=8.944 14. Which pair of angles could be the possible correct angle and reference angle of the angle in standard position pictured below? Malwarebytes16. Eric was creating a cubic model to describe the volume of a box created from 20 a 12" x 18" piece of cardboard, cutting out different size squares from the corners and folding up the sides. He drew the following diagram and created the equation for the volume of the box: v(x) = (12 - 4x)(18 - 4x)(2x). 18" X" X' 12" X' x" Is this picture correct? Is the equation correct? If not, explain why. What is the maximum volume to the nearest cubic inch you can obtain from a box created from this scenario? Explain how you arrived at your answer. BIUS Normal X2 fx Enter your response here alwarebytesLead term: 7x3 Degree: 3 O Leading coefficient: 7 f(x) -+-co as x-09 f(x) - 0 as x -+ co 5. Use the Rational Zero Theorem and synthetic division to find all real zeros: f (x) = 5x3 - 15x + 10 O X=-2,1 O X=-1,2 O X=-2, 1, 5 O X=-1, 2, 5 6. From the graph, write the equation of the polynomial function. 5 -2 -15 -0 5 0 0 5 15 25 3 35 MalwarebytesBFpa-n6irTZHtbzKZGODG IN PROGRESS Pre-Calculus Semester 1 Final cil 160 total points Multiple Choice (15 Questions) 1. Which function represents a cubic parent function shifted right 4, reflected on x, vertically stretched by 2, and shifted down 3? Of(z) = -25x+4-3 Of(z) =-232-4-3 Of(z) =-1Vo+4-3 Of(3) =-2V2-3-4 2. Find (go f) (3) from the graphs below. Malwarebytes16. Eric was creating a cubic model to describe the volume of a box created from 20 a 12" x 18" piece of cardboard, cutting out different size squares from the corners and folding up the sides. He drew the following diagram and created the equation for the volume of the box: v(x) = (12 - 4x)(18 - 4x)(2x). 18" X" X' 12" X' x" Is this picture correct? Is the equation correct? If not, explain why. What is the maximum volume to the nearest cubic inch you can obtain from a box created from this scenario? Explain how you arrived at your answer. BIUS Normal X2 fx Enter your response here alwarebytes\fAngle: 132', Reference angle: 42 Angle: 133, Reference angle: 33 Angle: 134, Reference angle: 46 Angle: 136, Reference angle: 46 15. What is the exact value of sin ( 211 )? O O O N/S Essay (5 Questions) Type your answer into the field below. 16 Crin Was describe the volume fahav fran alwarebytesAngle: 132, Reference angle: 420 O Angle: 133, Reference angle: 330 Angle: 134%, Reference angle: 46 O Angle: 136, Reference angle: 46 alwarebytes9. Find the inverse of the logarithmic function: f (a) = log2 (x - 3) +4 4 PO Of (z) =20-4+3 Of-1 (2) =20-3+4 Of-(2) =23-4-3 Of(2) =23-3 -4 10. Condense the following into a single logarithm using logarithmic properties: log; (6z) + 2log: (y) - 410g3 (z) O logs (6zy) log3 (2) O log3 12ay O logs (#-) O logs alwarebytes20. Solve the following show all of your work: The population in a small town is growing at a rate of 1.5% each year, how long will it take for the population to triple? BIUS Normal X2 X2 fx Enter your response here alwarebytesLead term: 7x3 Degree: 3 O Leading coefficient: 7 f(x) -+-co as x-09 f(x) - 0 as x -+ co 5. Use the Rational Zero Theorem and synthetic division to find all real zeros: f (x) = 5x3 - 15x + 10 O X=-2,1 O X=-1,2 O X=-2, 1, 5 O X=-1, 2, 5 6. From the graph, write the equation of the polynomial function. 5 -2 -15 -0 5 0 0 5 15 25 3 35 Malwarebytes4. Identify the lead term, degree, and leading coefficient of the following 4 PO polynomial function and describe the end behavior: f (x) = -3+723 -4x5 + x Lead term: - 4x Degree: 5 O Leading coefficient: -4 f(x) - 0 asx -+0 f(x) -co asx - 00 Lead term: -3 Degree: 0 Leading coefficient: -3 f(x ) - -0 asx -+00 f(x) - casx-+ 0 Lead term: x Degree: 1 O Leading coefficient: 1 f(x ) -0oasx -+00 f(x) - casx-+ co Lead term: 7x3 Degree: 3 O Leading coefficient: 7 f (x) - 00 asx - -0 f(x) - casx-+ co alwarebytes17. Lauren was asked to describe the end behavior of the power function f (x) = -3:6. She said that the graph would rise on the left side and fall on the right side and that f() would approach co as a approaches -co and that f(a) would approach -co as a approaches co. Determine if Lauren is correct in her description of the end behavior of the power function. Then correctly describe the end behavior of the function. BIUS Normal X2 X2 Enter your response here lalwarebytes6. From the graph, write the equation of the polynomial function. 4 PO -15 -05 0 0 5 15 2 25 3 35 Of(z) = 3(z +2)? (x - 1) 2 Of(z) =3(x -2) (x+1) Of(z) = -3(x - 2)2(x + 1)2 Of(x) = -3(x +2) (x -1) 7. Determine all intercepts and asymptotes of the rational function: f (z) 4(x-2)(2+1) (+2 1 ( 0- 1) alwarebytes