Finding Input Values for Functions

The video tutorial explains how to determine the value of K that satisfies the translation of a graph from f(x) to f(K*x). It focuses on understanding horizontal stretch by comparing points on the original and transformed graphs. Through examples, it demonstrates how to find K by analyzing input-output pairs, confirming that K equals 1/2.

What is the main goal of the problem discussed in the video?

• To find the maximum value of the function.

• To calculate the area under the graph.

• To determine the color of the graph lines.

• To find the value of K that satisfies the translation of the graph.

What does a horizontal stretch in a graph involve?

• Changing the color of the graph.

• Changing the output values.

• Changing the input values.

• Changing the slope of the graph.

In the first example, what input value for f(Kx) gives the same output as an input of 3 for f(x)?

• 2

• 4

• 6

• 8

What conclusion is drawn from the first example regarding the value of K?

• K = 1

• K = 3

• K = 1/2

• K = 2

What is the output value for f(x) when the input is 3 in the first example?

• 6

• 9

• 15

• 12

In the second example, what input value for f(Kx) gives the same output as an input of 4 for f(x)?

• 10

• 12

• 8

• 6

What is the consistent conclusion about the value of K from both examples?

• K = 1

• K = 2

• K = 3

• K = 1/2

How is the input value changed in a horizontal stretch?

• It is multiplied by K.

• It is divided by K.

• It is added to K.

• It is subtracted from K.

What is the output value for f(Kx) when the input is 8 in the second example?

• 12

• 14

• 18

• 16

What mathematical operation is used to determine the value of K in the examples?

• Addition

• Subtraction

• Division

• Multiplication