Question

State the various transformations applied to the base function f(x) = x3 to obtain a graph of the function g(x) = 3(x + 4)3 -5

Answer 1

`f(x)=x^3`
`f(x+c)`

horizontally shifts the graph of f(x) left by c units.

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`f(x)-k`

vertically shifts the graph of f(x) down by c units.

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`a\cdot f(x)`

vertically stretches the graph of f(x) by a factor of a units.

Therefore:

`g(x)=3(x+4)^3-5`

it is the graph f(x) stretched vertically by a factor of 3, shifted down vertically by 5 units, and shifted horizontally 4 units to the left