Determine the coordinates of the image of D(4, −3) under the following translations. 1. (x, y) → (x + 3, y)
2. Translated down 5 units
3. Translated left 2 units and up 1 unit
4. (x, y) → (x − 4, y − 8)

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Step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.