Wrics 3 Quarter CC \#5 \( f(x)=2^{\mathrm{x}} \) after a vertical stretch by a factor of 3 and a reflection across the \( x \)-axis. Graph both functions. Writion \( g(x) \) that represents the exponential function

It seems that the system does not currently support plotting functions. However, I can describe how to graph both functions. ### Steps to Graph the Functions 1. **Graph \( f(x) = 2^x \)**: - This is an exponential growth function. - It passes through the point (0, 1) because \( 2^0 = 1 \). - As \( x \) increases, \( f(x) \) increases rapidly. - As \( x \) decreases, \( f(x) \) approaches 0 but never touches the x-axis (asymptote at \( y = 0 \)). 2. **Graph \( g(x) = -3 \cdot 2^x \)**: - This function is a reflection of \( f(x) \) across the x-axis and vertically stretched by a factor of 3. - It passes through the point (0, -3) because \( g(0) = -3 \cdot 2^0 = -3 \). - As \( x \) increases, \( g(x) \) decreases rapidly (since it is negative). - As \( x \) decreases, \( g(x) \) approaches 0 from below (asymptote at \( y = 0 \)). ### Summary of the Graphs - **\( f(x) = 2^x \)**: Exponential growth, passing through (0, 1), approaching 0 as \( x \) decreases. - **\( g(x) = -3 \cdot 2^x \)**: Exponential decay (reflected), passing through (0, -3), approaching 0 as \( x \) decreases. You can use graphing software or a graphing calculator to visualize these functions based on the descriptions provided. If you have any further questions or need additional assistance, feel free to ask!