Question

Graph the functions as transformations of f ( x ) = x

Answer 1

Since the functions are not included, I can help you with some examples and a  general explanations which will help you to solve this kind of problems.


1) Assumption: all the functions that are considered are linear.


That means that f(x) = x is the parent function, and you can obtain the other functions by a set of transformations (translation and scalation) of the parent function.

2) Example 1: y = x + a


This is a special case of adding a constant to the function.

In this case, the graph of the new function is the graph of the parent function shifted a units upward.

3) Example: y = 5x

This is a special case of multiplying the function times a constant.

The result is streching the graph vertically by the same scale factor.

4) Example: y = (1/5)x - 8

In this case, the graph of y is obtained by scaling the parent function f(x) = x by 1/5 (which results in compressing the parent function vertically) and shifting the parent function 8 units downward.