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

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

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.

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

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.

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.

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