Graphing Functions and Transformations

The video tutorial explores graph transformations by analyzing changes between functions. Initially, Alex graphs F(x) and G(x), identifying a horizontal compression as G(x) increases faster. Gabby then graphs H(x) and K(x), noting a horizontal stretch as K(x) decreases slower. The tutorial emphasizes understanding these transformations and their visual impacts on function graphs.

What was the initial task given to Alex in the video?

• To find the derivative of G(x).

• To solve an equation involving F(x).

• To graph F(x) and G(x) and analyze the transformation.

• To compare F(x) with a constant function.

What is the first step Alex took to solve the problem?

• He calculated the derivative of F(x).

• He compared F(x) with G(x) directly.

• He graphed the function F(x).

• He solved for the roots of F(x).

What transformation was observed from F(x) to G(x)?

• Vertical stretch

• Horizontal compression

• Translation to the right

• Reflection over the x-axis

What was Gabby's task in the video?

• To find the derivative of K(x).

• To solve an equation involving H(x).

• To compare H(x) with a constant function.

• To graph H(x) and K(x) and analyze the transformation.

What is the first step Gabby took to solve her problem?

• She calculated the derivative of H(x).

• She graphed the function H(x).

• She compared H(x) with K(x) directly.

• She solved for the roots of H(x).

What transformation was observed from H(x) to K(x)?

• Translation to the left

• Vertical compression

• Horizontal stretch

• Reflection over the y-axis

How did Gabby manipulate the second function to demonstrate the horizontal stretch?

• By multiplying the function by a constant.

• By adding a constant to the function.

• By changing the base of the exponent.

• By reflecting it over the x-axis.

What is the effect of a horizontal stretch on the rate of increase of a function?

• It increases the rate of increase.

• It decreases the rate of increase.

• It has no effect on the rate of increase.

• It makes the function constant.