Question

if (v) is an independent variable and (w) is a variable thats dependent on (v), which of the following could be function - notation representations of (w). select all that apply. select all that apply: (f(v)=2v - 1) (f(w)=9 - 3w) (f(v)=1 - 8v) (f(v)=9 - 3w)

Explanation:

Step1: Recall function - notation concept

In function notation $y = f(x)$, $x$ is the independent variable and $y$ is the dependent variable. Here $v$ is independent and $w$ is dependent.

Step2: Analyze each option

• Option A: $f(v)=2v - 1$ can represent $w$ as a function of $v$. Here $w$ could be equal to $2v - 1$.
• Option B: $f(w)=9 - 3w$ has $w$ as the independent variable in the function - notation, which is incorrect as $w$ is the dependent variable.
• Option C: $f(v)=1 - 8v$ can represent $w$ as a function of $v$. Here $w$ could be equal to $1 - 8v$.
• Option D: $f(v)=9 - 3w$ is a valid form where $w$ is related to $v$ in the right - hand side of the equation and $v$ is the independent variable in the function notation.

Answer:

A. $f(v)=2v - 1$, C. $f(v)=1 - 8v$, D. $f(v)=9 - 3w$