Question

The function f(x) = xis translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)?

Answer 1

Answer:

$g(x)=x+4$

Step-by-step explanation:

Given

$f(x)=x$

$g(x)\rightarrow f(x)$ shifted 7 units left  and 3 units down

Translation Rules:

$f(x)\rightarrow f(x+c)$

If $c>0$ the function shifts $c$ units to the left.

If $c$ the function shifts $c$ units to the right.

$f(x)\rightarrow f(x)+c$

If $c>0$ the function shifts $c$ units to the up.

If $c$ the function shifts $c$ units to the down.

Applying the rules to $f(x)$

$f(x)\rightarrow f(x+7)$            [7 units left]

$f(x+7)\rightarrow f(x+7)-3$    [3 units down]

∴ $g(x)=f(x+7)-3=(x+7)-3=x+7-3=x+4$

$g(x)=x+4$