Understanding Function Transformations

The video tutorial explains how to transform the function f(x) = |x| into a new function G(x) by flipping it over the x-axis and stretching it vertically. The process involves understanding the effects of these transformations on the graph of the function. The tutorial also explores an alternative approach to achieve the same transformation, emphasizing the flexibility in mathematical problem-solving.

What is the initial function f(x) that is being transformed to create G(x)?

• f(x) = 1/x

• f(x) = x^3

• f(x) = |x|

• f(x) = x^2

What happens to the function f(x) when it is flipped over the x-axis?

• It becomes negative

• It becomes a horizontal line

• It becomes positive

• It remains unchanged

What is the purpose of flipping the function over the x-axis?

• To make the function positive

• To make the function negative

• To make the function constant

• To make the function zero

How is the function stretched or compressed to match G(x) when x = 1?

• By multiplying by 2

• By multiplying by 5

• By multiplying by 3

• By multiplying by 4

What is the effect of multiplying the function by four?

• It flips the function over the y-axis

• It compresses the function horizontally

• It shifts the function upwards

• It stretches the function vertically

What is the key transformation needed to achieve G(x) from the green function?

• Adding a constant

• Multiplying by a constant

• Dividing by a constant

• Subtracting a constant

What is the alternative approach to transforming f(x) to G(x)?

• First stretch, then flip

• First compress, then shift

• First shift, then stretch

• First flip, then stretch

What is the final form of G(x) after all transformations?

• G(x) = 4|x|

• G(x) = -4x

• G(x) = 4x

• G(x) = -4|x|

What does the negative sign in the transformation indicate?

• A reflection over the y-axis

• A reflection over the x-axis

• A vertical shift

• A horizontal shift

What is the result of applying both stretching and flipping transformations?

• A horizontal line

• A vertical line

• A transformed function G(x)

• An unchanged function