Question

choose the graph of the function ( f(x) = 3x ) and its parent function.
four graphs with options (circles) and labeled axes, lines
describe the transformation.

Explanation:

Step1: Identify Parent Function

The parent function of \( f(x) = 3x \) is \( y = x \) (linear parent function), which passes through the origin with a slope of 1.

Step2: Analyze \( f(x) = 3x \)

The function \( f(x) = 3x \) is a linear function with slope 3, also passing through the origin. A slope of 3 means it is steeper than \( y = x \) (slope 1).

Step3: Match Graphs

• The first graph: The red line has a y - intercept (not through origin), so incorrect.
• The second graph: Both lines pass through the origin. The red line ( \( f(x)=3x \)) is steeper than the blue line ( \( y = x \)), which matches.
• The third graph: The red line is less steep, incorrect (should be steeper).
• The fourth graph: The red line is less steep, incorrect.

For the transformation: The function \( f(x)=3x \) is a vertical stretch (or horizontal compression) of the parent function \( y = x \) by a factor of 3, since the coefficient of \( x \) is greater than 1, making the line steeper.

Answer:

The correct graph is the second one (with both lines through the origin, red line \( f(x) = 3x \) steeper than blue \( y = x \)). The transformation is a vertical stretch (by factor 3) of the parent function \( y = x \).