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
Hey ThEe, good to see you again. Here are the solutions to the problems based on the given exponential function y = ((1)/(2))^x - 4. Step 1: Determine the coordinates of A (y-intercept). The y-intercept occurs when x=0. Substitute x=0 into the equation: y = ((1)/(2))^0 - 4 y = 1 - 4 y = -3 The coordinates of A are (0, -3). Step 2: Determine the coordinates of B (x-intercept). The x-intercept occurs when y=0. Substitute y=0 into the equation: 0 = ((1)/(2))^x - 4 4 = ((1)/(2))^x Rewrite 4 as a power of 2 and (1)/(2) as a power of 2: 2^2 = (2^-1)^x 2^2 = 2^-x Equate the exponents: 2 = -x x = -2 The coordinates of B are (-2, 0). Step 3: Equation of the asymptote of y. For an exponential function of the form y = ab^x + c, the horizontal asymptote is y=c. In the given equation y = ((1)/(2))^x - 4, the value of c is -4. The equation of the asymptote is y = -4. Step 4: Domain and range of y. The domain of an exponential function is all real numbers. The range is determined by the horizontal asymptote. Since the base (1)/(2) is between 0 and 1, the function decreases and approaches the asymptote y=-4 from above. The domain is x R. The range is y > -4. Send me the next one 📸