Question

1. describe, using mapping notation, how the graphs of the following functions can be obtained from the graph of \\(y = f(x)\\).

a) \\(y = f(x + 10)\\)

Explanation:

Identify the transformation

We analyze the function \(y = f(x + 10)\).
Using the Function Transformations concept, we identify the change inside the argument.
The input \(x\) is replaced by \(x + 10\).

Determine horizontal shift

Using the Horizontal Translation concept, we find the shift direction.
Replacing \(x\) with \(x + 10\) shifts the graph left by 10 units.
This means each original point \((x, y)\) moves to \((x - 10, y)\).

Express in mapping notation

Mapping notation describes how coordinates transform.
The original coordinates are \((x, y)\).
The transformed coordinates are \((x - 10, y)\).
Thus, the mapping is \((x, y)
ightarrow (x - 10, y)\).

Answer:

Describe, using mapping notation, how the graph of \(y = f(x + 10)\) can be obtained from the graph of \(y = f(x)\).

The mapping notation is <blank>\((x, y)
ightarrow (x - 10, y)\)</blank>.