Math 104 Fall 2024 Quiz II Review Sheet PDF

Math 104-Fall 2024 Review Sheet for Quiz II Sections 3.1, 3.2, 3.3, 4.2& 4,2 Question 1 If the point (−𝑎, 𝑏) lies in quadrant IV, then in which quadrant lies the reflection of the point (𝑎, 𝑏) with respect to the origin? Question 2 Determine whether the points 𝑃 2 + 2, 3 − 3 , 𝑄 4 + 2, 5 − 3 an...

Math 104-Fall 2024 Review Sheet for Quiz II Sections 3.1, 3.2, 3.3, 4.2& 4,2 Question 1 If the point (−𝑎, 𝑏) lies in quadrant IV, then in which quadrant lies the reflection of the point (𝑎, 𝑏) with respect to the origin? Question 2 Determine whether the points 𝑃 2 + 2, 3 − 3 , 𝑄 4 + 2, 5 − 3 and 𝑅( 2, 1 − 3) are collinear or not.  Question 3 Determine whether the points (0,2); (2,0) and (5,3) are the vertices of a right triangle or not.  3 Question 4 Find the value of 𝑥 for which the point 𝑀 , −1 is the midpoint of 2 𝑥 the line segment joining the points 𝐴(2𝑥 − 1, −4) and 𝐵 ,2. 3 Question 5 Determine whether the point (2,1) is on the graph of the equation 𝑦 − 𝑥 2 − 2 = 1 or not. Question 6 Find the intercepts of the equation (𝑥 + 1)|𝑦| + 𝑥 2 = 5|𝑦| + 4. Question 7 Test the graph of the equation 𝑥𝑦 2 + 𝑦 = 𝑥 + 3 for symmetry. Question 8 Given the line 𝐿1 : 3𝑥 − 4𝑦 = 5, let 𝐿2 ​ be the line that is parallel to 𝐿1 ​ and passes through the point (−2,4). Let 𝐿3 ​ be the line that is perpendicular to 𝐿1 and passes through the point (1, −1). Write the standard form equation for each of the lines 𝐿2 and 𝐿3 ​. Question 9 The graph of line 𝐿1 is shown in the figure below. Let 𝐿2 ​ be the line that is parallel to 𝐿1 ​ and passes through the point (−2,3). Let 𝐿3 ​ be the line that is perpendicular to 𝐿1 and passes through the point (2, −3). Write the standard form equation for each of the lines 𝐿1 , 𝐿2 and 𝐿3 ​. Question 10 1) For each of the following, determine whether the relation defines 𝑦 as a function of 𝑥 or not. a) 1, 2 , 2, −1 , 3, 5 , −3, 2 , −2, 0 , −1, 5 , (−2,5) b) 𝑦 2 ≥ 𝑥 + 1 c) + 𝑥 − 1 = 1 2) Sketch a graph on a coordinate system of a relation that is not a function. Question 11 1) The domain of the function 𝑓 is: 2) The range of the function 𝑓 is: 3) The interval where the function 𝑓 is increasing, is: 4) The interval where the function 𝑓 is decreasing, is: Question 11 5) The interval where the function 𝑓 is constant, is: 6) The 𝑦-intercept of the function 𝑓 is: 7) The image of −2 by 𝑓 is: 𝑓(−2) = 8) The solution of the equation 𝑓(𝑥) = 3, is 𝑥 =.... Question 11 5) The interval where the function 𝑓 is constant, is: 6) The 𝑦-intercept of the function 𝑓 is: 7) The image of −2 by 𝑓 is: 𝑓(−2) = 8) The solution of the equation 𝑓(𝑥) = 3, is 𝑥 =.... Question 12 1) Sketch the graph of the piecewise defined function 𝑥 if 𝑥≥2 𝑓 𝑥 = ቐ |𝑥| if −1 ≤ 𝑥 < 2. −1 if 𝑥 < −1 We give 2 ≃ 1.41. 2) Evaluate 𝑓(−2), 𝑓(−1), 𝑓(1) and 𝑓(2).