1. **Skill #1: Function Tables** **Function #1: $f(x) = 12 - 3x$** - Given $x=4$, find $y$: $$y = 12 - 3(4) = 12 - 12 = 0$$ - Given $y=18$, find $x$: $$18 = 12 - 3x$$ $$18 - 12 = -3x$$ $$6 = -3x$$ $$x = \frac{6}{-3} = -2$$ **Function #2: $f(x) = 3(x + 2) - 5x$** - Given $x = -3$, find $y$: $$y = 3(-3 + 2) - 5(-3) = 3(-1) + 15 = -3 + 15 = 12$$ - Given $y = 0$, find $x$: $$0 = 3(x + 2) - 5x$$ $$0 = 3x + 6 - 5x$$ $$0 = -2x + 6$$ $$-6 = -2x$$ $$x = \frac{-6}{-2} = 3$$ 2. **Skill #2: Solving for a Variable** a) Solve $s = \frac{(u + v)t}{2}$ for $u$: - Multiply both sides by 2: $$2s = (u + v)t$$ - Divide both sides by $t$: $$\frac{2s}{t} = u + v$$ - Subtract $v$ from both sides: $$u = \frac{2s}{t} - v$$ b) Solve $y = \frac{1}{2}x + 12$ for $x$: - Subtract 12 from both sides: $$y - 12 = \frac{1}{2}x$$ - Multiply both sides by 2: $$2(y - 12) = x$$ - Simplify: $$x = 2y - 24$$ c) Solve $b = \frac{a - c}{8}$ for $a$: - Multiply both sides by 8: $$8b = a - c$$ - Add $c$ to both sides: $$a = 8b + c$$ 3. **Skill #3: What is a function?** - A function is a relationship where each element of the input (**domain**) produces exactly one output (**range**).