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: Use the y-intercept to find q. The function is given by f(x) = p^x + q. Point B(0;-3) is the y-intercept of f. This means when x=0, f(x)=-3. Substitute these values into the equation: -3 = p^0 + q Since any non-zero number raised to the power of 0 is 1 (p ≠ 0 for an exponential function): -3 = 1 + q Subtract 1 from both sides: q = -3 - 1 q = -4 Step 2: Use point A(3;4) and the value of q to find p. Point A(3;4) is a point on the graph of f. This means when x=3, f(x)=4. Substitute x=3, f(x)=4, and q=-4 into the equation f(x) = p^x + q: 4 = p^3 + (-4) 4 = p^3 - 4 Add 4 to both sides: 4 + 4 = p^3 8 = p^3 Take the cube root of both sides: p = [3]8 p = 2 The values are p = 2 and q = -4. 3 done, 2 left today. You're making progress.