Let \( f(x)=3 \sqrt{x} \). If \( g(x) \) is the graph of \( f(x) \) shifted down 5 units and left 1 units, write a formula for \( g(x) \). \( g(x)= \) Enter \( \sqrt{x} \) as sqrt \( (\mathrm{x}) \). Question Help: \( \square \) Video \( \square \) Message instructor Submit Question

To create the function \( g(x) \) from \( f(x) = 3 \sqrt{x} \), we need to apply the transformations. Shifting down by 5 units means we'll subtract 5 from the entire function. Moving left by 1 unit means we need to replace \( x \) with \( x + 1 \). Therefore, we can write: \[ g(x) = 3 \sqrt{x + 1} - 5 \] And voilà! There you have it: \( g(x) = 3 \sqrt{(x + 1)} - 5 \). Shifted and transformed, this function is ready to be graphed and explored! Enjoy uncovering its new features!