State the order and type of each transformation of the graph of the function ƒ(x) = 4(5x)3 – 6 as compared to the graph of the base function

For the function, [tex]f(x) = 4(5x^3) -6[/tex], stretches the graph by making the outputs matched to the inputs much larger than the parent function [tex]f(x) = x^3[/tex]. It stretches further by being multiplied by 4 after [tex]5^3=125[/tex]. Lastly the graph is shifted down by 6 units.

Step-by-step explanation:

When functions are transformed there are a few simple rules:

Adding/subtracting inside the parenthesis to the input shifts the function left(+) and right(-).
Adding/subtracting outside the parenthesis to the output shifts the function up(+) and down(-).
Multiplying the function by a number less than 1 compresses it towards the x-axis.
Multiplying the function by a number greater than 1 stretches it away from the x-axis.
Multiplying by a negative or changing the leading coefficient's sign will flip the graph.

For the function, [tex]f(x) = 4(5x^3) -6[/tex], stretches the graph by making the outputs matched to the inputs much larger than the parent function [tex]f(x) = x^3[/tex]. It stretches further by being multiplied by 4 after [tex]5^3=125[/tex]. Lastly the graph is shifted down by 6 units.