Question

which results only in a horizontal compression of (y = \frac{1}{x}) by a factor of 6?

\\(y = \frac{1}{6x}\\)

\\(y = -\frac{1}{6x}\\)

\\(y = \frac{6}{x}\\)

\\(y = -\frac{6}{x}\\)

Explanation:

⚡ Using what you learned: combining transformations

Step 1: Identify the rule for horizontal compression

A horizontal transformation affects the input variable \( x \) directly inside the function. For any function \( f(x) \), replacing \( x \) with \( c \cdot x \) (where \( c > 1 \)) results in a horizontal compression by a factor of \( c \).

$$ f(x) \to f(c \cdot x) $$

Step 2: Apply the transformation to the parent function

The parent function is:

$$ y = \frac{1}{x} $$

To compress the graph horizontally by a factor of \( 6 \), we substitute \( x \) with \( 6x \):

$$ y = \frac{1}{6x} $$

Answer:

$$ y = \frac{1}{6x} $$