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

To sketch the graph of the function \( y = 4.3^{3x} \), we can start by understanding the properties of the function. Given function: \( y = 4.3^{3x} \) 1. **Domain**: The domain of the function is all real numbers, since the base of the exponent is a positive number and the exponent is a real number. 2. **Range**: The range of the function is all positive real numbers, since the base of the exponent is greater than 1 and the exponent is a real number. 3. **Asymptotes**: The function has a horizontal asymptote at \( y = 0 \), since as \( x \) approaches negative infinity, \( y \) approaches 0. 4. **Intercepts**: The function has a y-intercept at \( (0, 1) \), since when \( x = 0 \), \( y = 4.3^{3*0} = 1 \). 5. **Increasing/Decreasing**: The function is increasing for all values of \( x \), since the base of the exponent is greater than 1. 6. **Symmetry**: The function is symmetric about the y-axis, since the function is even. 7. **Graph**: The graph of the function will be a curve that starts at the y-intercept and increases as \( x \) increases, approaching the horizontal asymptote at \( y = 0 \) as \( x \) approaches negative infinity. To sketch the graph, you can start by plotting the y-intercept at \( (0, 1) \) and then plot a few more points by substituting different values of \( x \) into the function. You can also use a graphing calculator or software to visualize the graph.