Final answer:
The transformation described by t(x) = 3p(x + 2) + 4 is a scaling by 3, a horizontal shift right by 2 units, and a vertical shift up by 4 units. To find the elasticity of a supply curve between two prices, one would use the price elasticity of supply formula, involving the supply equation P = 3Q - 8. Geometrically, rotation transforms coordinates using trigonometric functions as shown by the given relations for x' and y'.
Step-by-step explanation:
The question asks about describing the transformation represented by a given mathematical relationship, where t(x) is defined in terms of p(x). The relationship is given as t(x) = 3p(x + 2) + 4. To describe the transformation, we first note that p(x) is scaled by a factor of 3 and then shifted right by 2 units along the x-axis, which is indicated by the x + 2 inside the function p. Lastly, the entire function is then shifted upwards by 4 units on the y-axis, as indicated by the +4 outside the function.
The elasticity of a supply curve from a price of 4 to a price of 7 can be calculated by using the formula for price elasticity of supply (PES), which is the percentage change in quantity supplied divided by the percentage change in price. This calculation involves determining the change in quantity, Q, that corresponds to the change in price from 4 to 7 using the supply equation P = 3Q - 8 and then applying the formula for PES.
In terms of geometrical transformations, the concept of rotation was explained by showing how the coordinates transform using trigonometric functions. The rotation transformation is expressed as x' = x cos q + y sin o and y' = -x sin p + y cos p, where x' and y' are the new coordinates after rotation, and x and y are the original coordinates.