1. Problem statement: The goal is to use $y$ instead of $f(x)$ to name a function and to show how to rewrite, evaluate, and solve for variables. 2. Formula and rules: A function written as $f(x)$ can be equally written as $y$ by defining $$y=f(x)$$. When you replace $f(x)$ with $y$, every occurrence of $f(x)$ is replaced by $y$ and algebraic manipulations follow the same rules. 3. Example 1: Rewriting. Given $f(x)=2x^2+3x-5$ rewrite as $$y=2x^2+3x-5$$. Evaluate at $x=2$: $$y=2(2)^2+3(2)-5$$. Compute: $$y=8+6-5$$. Therefore $$y=9$$. 4. Example 2: Solving for $x$. Given $$y=2x+4$$ solve for $x$. Subtract 4 from both sides to isolate the term with $x$: $$y-4=2x$$. Divide both sides by 2 to solve for $x$: $$\frac{2x}{2}=\frac{y-4}{2}$$. Show cancellation of the common factor 2: $$\frac{\cancel{2}x}{\cancel{2}}=\frac{y-4}{2}$$. So $$x=\frac{y-4}{2}$$. 5. Important notes: Using $y$ is a notational change only and does not affect domain, evaluation, or algebraic rules. If a function uses another name like $f(t)$ or $g(x)$ you can similarly set $y=f(t)$ or $y=g(x)$ and proceed. 6. Final answer: To use $y$ write $$y=f(x)$$ and then perform algebra and evaluation exactly as you would with $f(x)$.