Question

let \\( f(x) = 4\sqrt{x} \\)

if \\( g(x) \\) is the graph of \\( f(x) \\) shifted down 4 units and left 5 units, write a formula for \\( g(x) \\)

\\( g(x) = \\)

enter \\( \sqrt{x} \\) as sqrt(x)

Explanation:

Apply horizontal shift

$$ f(x + 5) = 4\sqrt{x + 5} $$

Apply vertical shift

$$ g(x) = f(x + 5) - 4 = 4\sqrt{x + 5} - 4 $$

Format for input

$$ g(x) = 4\text{sqrt}(x + 5) - 4 $$

Answer:

Let \(f(x) = 4\sqrt{x}\).

If \(g(x)\) is the graph of \(f(x)\) shifted down 4 units and left 5 units, write a formula for \(g(x)\)

\(g(x) =\) <blank>\(4\text{sqrt}(x+5)-4\)</blank>