1. 8-5 Variation Functions
Recognize and solve direct and joint variation problems.
Recognize and solve inverse and combined variation problems

2. Direct variation: expressed in form 𝑦=𝑘𝑥
Direct variation: expressed in form 𝑦=𝑘𝑥. K is the constant of variation (think slope) and there CANNOT be anything added on. Graph goes through the origin. “y varies directly with x”
Two parts: write an equation, solve for what is requested.

3. Give the equation of variation (find k) and solve for the unknown quantity.

4. Joint variation: when one quantity varies directly as the product of two or more quantities. “y varies jointly with x and z means 𝑦=𝑘𝑥𝑧
Give the equation of variation (find k) and solve for the unknown quantity.

5. Inverse variation: The product of two quantities is a constant, or as one gets larger, the other gets smaller. 𝑦= 𝑘 𝑥 𝑜𝑟 𝑥𝑦=𝑘 (graph is a hyperbola, that is, a reciprocal function!)
Give the equation of variation (find k) and solve for the unknown quantity.

6. Combination: one quantity varies directly/ and or inversely with other quantities.
Give the equation of variation (find k) and solve for the unknown quantity.