Let $$ f(x)=4 \sqrt{x} $$. If $$ g(x) $$ is the graph of $$ f(x) $$ shifted up 6 units and left 3 units, write a formula for $$ g(x) $$. $$ g(x)=\square $$ Enter $$ \sqrt{x} $$ as sqrt(x).

Question

UpStudy AI · Accepted Answer

We start with the function  
$$
f(x)=4\sqrt{x}.
$$

The graph $$ g(x) $$ is obtained by shifting $$ f(x) $$ up 6 units and left 3 units.

1. Shifting left by 3 units means replacing $$ x $$ with $$ x+3 $$ in the function. Thus, we get:
   $$
   f(x+3)=4\sqrt{x+3}.
   $$

2. Shifting up by 6 units means adding 6 to the function. Therefore, the function becomes:
   $$
   g(x)=4\sqrt{x+3}+6.
   $$

Thus, the formula for $$ g(x) $$ is  
$$
g(x)=4\sqrt{x+3}+6.
$$
$$ g(x) = 4\sqrt{x + 3} + 6 $$

Let \( f(x)=4 \sqrt{x} \). If \( g(x) \) is the graph of \( f(x) \) shifted up 6 units and left 3 units, write a formula for \( g(x) \). \( g(x)=\square \) Enter \( \sqrt{x} \) as sqrt(x).

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Algebra Questions