Question

Write a function g(x) that transforms f(x)=4x³-5 of the following ways

a) Move 2 units left and reflect across the x-axis
b) Compress horizontally by a factor of 1/5 and move 1 unit up
c) Stretch vertically by a factor of 3 and move 3 units up

Answer 1

The function f(x)=4x³-5 can be transformed in various ways to create a new function g(x). Three distinct transformations include moving the function 2 units left and reflecting across the x-axis, compressing it horizontally by a factor of 1/5 and moving 1 unit up, and stretching it vertically by a factor of 3 and moving 3 units up. For each transformation, the function is adjusted accordingly to reflect the described changes.

Step-by-step explanation:

The transformation of a function f(x)=4x³-5 involves applying a set of operations to the function to obtain a new function g(x). We can apply the following transformations as described:

• Move 2 units left and reflect across the x-axis: g(x) = -f(x+2)
• Compress horizontally by a factor of 1/5 and move 1 unit up: g(x) = f(5x) + 1
• Stretch vertically by a factor of 3 and move 3 units up: g(x) = 3f(x) + 3

To apply these transformations, we substitute and simplify as follows:

1. For moving 2 units left and reflecting across the x-axis, g(x) = -(4(x+2)³-5).
2. For a horizontal compression by a factor of 1/5 and moving 1 unit up, g(x) = 4(5x)³-5 + 1.
3. For a vertical stretch by a factor of 3 and moving 3 units up, g(x) = 3(4x³-5) + 3.

The resulting functions represent the new transformations of f(x).