This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to your questions: QUESTION 1 1.1 Given xy = 2: 1.1.1 Sketch the graph of xy = 2. The equation xy = 2 can be rewritten as y = (2)/(x). This is a hyperbola. The graph has two branches: One branch is in the first quadrant (where x > 0 and y > 0). It passes through points like (1, 2) and (2, 1). The other branch is in the third quadrant (where x < 0 and y < 0). It passes through points like (-1, -2) and (-2, -1). The graph has a vertical asymptote at x=0 (the y-axis) and a horizontal asymptote at y=0 (the x-axis). The branches approach these axes but never touch them. 1.1.2 Is this graph a function or a relation? A function is a relation where each input (x-value) corresponds to exactly one output (y-value). For y = (2)/(x), for every x (except x=0), there is only one unique y value. This graph passes the vertical line test. Therefore, it is a function. 1.1.3 Is this graph continuous or discontinuous? A graph is continuous if it can be drawn without lifting the pen. The graph of y = (2)/(x) has a break at x=0 due to the vertical asymptote. Therefore, it is discontinuous. That's 2 down. 3 left today — send the next one.