Transformations of Linear Functions

The video tutorial explains how multiplying the function f(x) = x^2 by 2 affects its graph. The instructor guides viewers through identifying which line on a graph represents the transformed function, emphasizing that the yellow line is steeper due to the multiplication. The tutorial highlights the importance of understanding how transformations impact graph steepness and intersection points.

What happens to the graph of f(x) = x^2 when it is replaced by 2 * f(x)?

• It becomes narrower.

• It remains unchanged.

• It becomes wider.

• It shifts to the right.

Which lines intersect at the origin (0,0) after the transformation?

• Only the yellow line.

• Only the green line.

• The green and yellow lines.

• Only the black line.

How does the yellow line compare to the green line after the transformation?

• The yellow line is wider.

• The yellow line is narrower.

• The yellow line is steeper.

• The yellow line is flatter.

What characteristic of the yellow line indicates it represents 2 * f(x)?

• It is below the original line.

• It has a steeper slope.

• It is parallel to the original line.

• It intersects the x-axis at a different point.

Why does the yellow line represent the correct transformation of the function?

• Because it is the same as the original line.

• Because it is wider than the original line.

• Because it is the only line that intersects the y-axis.

• Because it shows values increasing much faster.

Which line does not increase two times as fast as the original function?

• The red line.

• The yellow line.

• The green line.

• The black line.