Question

find g(x), where g(x) is the translation 1 unit left of f(x) = 7x + 1.
$g(x) = 7x$
$g(x) = 7x + 2$
$g(x) = 7x + 8$
$g(x) = 7x - 6$

Explanation:

Step1: Recall left translation rule

For a left shift of $h$ units, $g(x)=f(x+h)$

Step2: Substitute $h=1$ into $f(x)$

$g(x)=f(x+1)=7(x+1)+1$

Step3: Simplify the expression

$g(x)=7x+7+1=7x+8$

Answer:

$g(x) = 7x + 8$