Question

F(x)=2x is transformed to g(x)=5⋅2x. How was the graph affected?

shifted up by 5 units

shifted down by 5 units

stretched by a factor of 5 units

compressed by a factor of 5 units

Answer 1

vertically stretched by a factor of 5

Explanation:

Multiplying the function value by 5 makes each vertical coordinate 5 times the value it was, so it is 5 times as far away from the x-axis. This has the appearance of stretching the graph vertically by a factor of 5.

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Comment on the answer choices

The stretch factor is a "pure number", a ratio of new units to old units. It is "5", not "5 units."

For example, if f(x) is 1 ft (1 unit, where the unit is a foot), then g(x) = 5 ft, the value of f(x) multiplied by 5. It is not 5 ft^2, as you would get if f(x) were multiplied by 5 units, or 5 ft.