Question

42 suppose $f(x) = -3x - 5$. if $g(x)$ represents the graph of $f(x)$ translated up 7 units, what is the equation of $g(x)$? a. $g(x) = -3x - 12$ b. $g(x) = -3x + 2$ c. $g(x) = 4x - 5$ d. $g(x) = -10x - 5$

Explanation:

Step1: Recall vertical translation rule

For a function $y = f(x)$, translating it up by $k$ units gives $y = f(x)+k$.

Step2: Apply the rule to $f(x)$

Given $f(x)=-3x - 5$ and translating up 7 units, so $g(x)=f(x)+7$.
Substitute $f(x)$: $g(x)=(-3x - 5)+7$.
Simplify: $g(x)=-3x+(-5 + 7)=-3x + 2$.

Answer:

B. $g(x) = -3x + 2$