Match each verbal description to its equivalent function rule as applied to the given function below. The function f stretched vertically by a factor of 4 and translated up by 9 units arrowBoth The function f translated 6 units up and 2 units rig

To match each verbal description to its equivalent function rule, we will denote the original function as \( f(x) \). Here are the function transformations based on the verbal descriptions provided: 1. **The function \( f \) stretched vertically by a factor of 4 and translated up by 9 units**: - This would be represented mathematically as: \[ g(x) = 4f(x) + 9 \] 2. **The function \( f \) translated 6 units up and 2 units right**: - When a function is translated to the right by \( h \) units and up by \( k \) units, the transformation is represented as: \[ g(x) = f(x - 2) + 6 \] 3. **The function \( f \) stretched vertically by a factor of 2 and translated up by 5 units**: - This can be expressed as: \[ g(x) = 2f(x) + 5 \] 4. **The function \( f \) reflected about the y-axis and translated 7 units left**: - To reflect about the y-axis, we replace \( x \) with \( -x \), and shifting left by \( h \) units requires the transformation \( f(x + 7) \): \[ g(x) = f(-x + 7) \] Now, let’s summarize the matching of verbal descriptions to their respective function rules: 1. **Stretched vertically by 4 and translated up by 9**: - \( g(x) = 4f(x) + 9 \) 2. **Translated 6 units up and 2 units right**: - \( g(x) = f(x - 2) + 6 \) 3. **Stretched vertically by 2 and translated up by 5**: - \( g(x) = 2f(x) + 5 \) 4. **Reflected about the y-axis and translated 7 units left**: - \( g(x) = f(-x) + 7 \) This allows us to accurately match each description with its corresponding function rule.