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
Step 1: Identify the general form of the function and its asymptotes. The given graph represents a hyperbola, which is a reciprocal function. The general form of such a function is y = (a)/(x-p) + q, where x=p is the vertical asymptote and y=q is the horizontal asymptote. From the graph: • The horizontal dashed line indicates the horizontal asymptote at y=4. So, q=4. • The graph approaches the y-axis but never touches it, indicating the vertical asymptote is the y-axis, x=0. So, p=0. Step 2: Substitute the asymptotes into the general equation. Using p=0 and q=4, the equation becomes: y = (a)/(x-0) + 4 y = (a)/(x) + 4 Step 3: Use the given point to find the value of a. The graph passes through the point F, which has coordinates (2, 10). Substitute x=2 and y=10 into the equation: 10 = (a)/(2) + 4 Step 4: Solve for a. Subtract 4 from both sides: 10 - 4 = (a)/(2) 6 = (a)/(2) Multiply both sides by 2: a = 6 × 2 a = 12 Step 5: Write the final equation. Substitute a=12 back into the equation from Step 2: y = (12)/(x) + 4 The equation of the function is y = (12)/(x) + 4. Send me the next one 📸