Effects of Input Transformation on Functions

The video tutorial explains how to transform the graph of f(x) = x^2 to f(2x) by multiplying the input by 2. It discusses the effect of this transformation on the graph, making it narrower and steeper. The tutorial compares different graphs to identify the correct transformation, focusing on specific points like (0,0) and (1,4) to determine that the red line represents f(2x). The video concludes by summarizing the transformation process and confirming the correct graph.

What is the initial function given in the problem?

• f(x) = x^3

• f(x) = x^2

• f(x) = 2x

• f(x) = x + 2

What happens to the graph when the input is multiplied by 2?

• The graph becomes narrower.

• The graph shifts upwards.

• The graph shifts to the right.

• The graph becomes wider.

Which lines are considered for the graph of f(2x)?

• Black and white lines

• Green and yellow lines

• Purple and orange lines

• Red and blue lines

What is the output when the input is 0 for both f(x) and f(2x)?

• 0

• 4

• 2

• 1

Which line is steeper, representing the graph of f(2x)?

• The red line

• The blue line

• The yellow line

• The green line

What is the output for f(2x) when the input is 1?

• 1

• 2

• 3

• 4

Which point confirms the red line as the correct graph for f(2x)?

• (2, 4)

• (1, 1)

• (3, 9)

• (0, 0)

How does multiplying the input by 2 affect the rate of increase and decrease of the graph?

• It reverses the rate.

• It slows down the rate.

• It speeds up the rate.

• It has no effect.

What would happen if the input was multiplied by 0.5 instead of 2?

• The graph would become steeper.

• The graph would become wider.

• The graph would remain unchanged.

• The graph would shift downwards.

Which line ultimately represents the graph of f(2x)?

• The red line

• The yellow line

• The blue line

• The green line