Question

"The equation for a polynomial function p(x) is given. The equation for the transformed function t(x) in terms of p(x) is also given. Describe the transformation(s) performed on p(x) that produced t(x). Then, write an equation for t(x) in terms of x."

a) Translation to the right by 3 units
b) Translation upwards by 3 units
c) Vertical compression by a factor of 2
d) Horizontal compression by a factor of 2

Answer 1

Transformations of a polynomial function p(x) to t(x) include translations and compressions. The transformation is applied to the original function, resulting in a new function expression for t(x) directly in terms of x.

Step-by-step explanation:

In algebra, transformations of functions can involve translations (shifts) and compressions (scaling). When a polynomial function p(x) undergoes a transformation to create t(x), the nature of the transformation can be determined by analyzing how the function has been altered.

• A translation to the right by 3 units would result in t(x) = p(x - 3).
• A translation upwards by 3 units would result in t(x) = p(x) + 3.
• A vertical compression by a factor of 2 would result in t(x) = ½p(x).
• A horizontal compression by a factor of 2 would result in t(x) = p(2x).

To write the equation for t(x) explicitly in terms of x, we apply the corresponding transformation to the original function p(x).