1 p(x) = 2^x - 8 is an exponential equation. 2.1.1 Calculate the x - intercept of p. 2.1.2 The y-intercept of p. 2.1.3 The asymptote(s) of p. 2.1.4 Draw a neat sketch of the graph of p.

Here are the calculations for the exponential function p(x) = 2^x - 8. 2.1.1 Calculate the x- intercept of p Step 1: To find the x-intercept, set p(x) = 0. 2^x - 8 = 0 Step 2: Isolate the exponential term. 2^x = 8 Step 3: Express both sides with the same base and solve for x. 2^x = 2^3 x = 3 The x-intercept is (3, 0). 2.1.2 The y- intercept of p Step 1: To find the y-intercept, set x = 0. p(0) = 2^0 - 8 Step 2: Calculate the value of p(0). p(0) = 1 - 8 p(0) = -7 The y-intercept is (0, -7). 2.1.3 The asymptote(s) of p Step 1: For an exponential function of the form y = a · b^x + k, the horizontal asymptote is y = k. In p(x) = 2^x - 8, the constant term is -8. The horizontal asymptote is y = -8. 2.1.4 Draw a neat sketch of the graph of p Since I cannot draw a graph directly, here are the key features for a neat sketch: • The graph is an increasing exponential function. • It passes through the x-intercept at (3, 0). • It passes through the y-intercept at (0, -7). • It has a horizontal asymptote at y = -8. • The graph approaches y = -8 as x approaches - and increases without bound as x approaches . Send me the next one 📸