Question

1. $f(x)=x + 7$; translation 5 units right

Explanation:

Step1: Recall translation rule

For a function $y = f(x)$, a translation $h$ units to the right gives $y=f(x - h)$. Here $h = 5$ and $f(x)=x + 7$.

Step2: Substitute into rule

Substitute $x$ with $x - 5$ in $f(x)$. So the new function is $f(x-5)=(x - 5)+7$.

Step3: Simplify the expression

$(x - 5)+7=x-5 + 7=x+2$.

Answer:

The new function is $f(x)=x + 2$.