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 is an analysis of the given functions: Function 1: h(x) = (1)/(x) - 4 Step 1: Identify the type of function and its asymptotes. This is a hyperbola. The vertical asymptote occurs where the denominator is zero. x = 0 The horizontal asymptote is determined by the constant term. y = -4 This function is a vertical translation of the parent function F(x) = (1)/(x) downwards by 4 units. Function 2: F(x) = (1)/(x) Step 2: Identify the type of function and its asymptotes. This is the parent hyperbola. The vertical asymptote occurs where the denominator is zero. x = 0 The horizontal asymptote is the constant term, which is 0 in this case. y = 0 Function 3: m(x) = -(8)/(x) + 2 Step 3: Identify the type of function and its asymptotes. This is a hyperbola. The vertical asymptote occurs where the denominator is zero. x = 0 The horizontal asymptote is determined by the constant term. y = 2 This function is a vertical stretch by a factor of 8, reflected across the x-axis, and then translated upwards by 2 units from the parent function F(x) = (1)/(x). That's 2 down. 3 left today — send the next one.