Sketch the gaph \( y=4.3^{3 x} \)

To sketch the graph of \( y = 4.3^{3x} \), start by noting that this is an exponential function where the base \( 4.3 \) is greater than \( 1 \). This means the function will increase rapidly as \( x \) increases. At \( x = 0 \), \( y = 4.3^{0} = 1 \), which gives you a point at \( (0, 1) \). For negative values of \( x \), the function will approach zero but never actually reach it, creating a horizontal asymptote on the x-axis. This means for \( x < 0 \), the values of \( y \) will be small. For positive \( x \), the curve will rise sharply as the exponent \( 3x \) increases. Plot more points like \( (1, 4.3^3) \) and \( (2, 4.3^6) \) to see how steeply the function climbs. Now, connect these points smoothly, keeping in mind the asymptotic behavior on the left and the rapid growth on the right. Overall, you'll create a curve that starts near the x-axis, passes through \( (0, 1) \), and rises steeply to the right. Happy sketching!