Graph Translation and Function Analysis

The video tutorial explains how to translate the graph of the function f(x) = 12x + 3 by replacing f(x) with f(x) + 5. It demonstrates moving each point on the graph up by five units and connecting them to form a new line. The tutorial also derives the new equation for the translated line, which is 12x + 8.

What is the initial function given in the video?

• f(x) = 12x + 3

• f(x) = 5x + 12

• f(x) = 12x - 3

• f(x) = 3x + 12

What is the initial y-intercept of the function f(x) = 12x + 3?

• 12

• 8

• 5

• 3

What operation is performed on each point of the graph?

• Move each point down by five units

• Move each point up by five units

• Move each point right by five units

• Move each point left by five units

How many units are the points moved in the translation?

• 3 units

• 6 units

• 5 units

• 4 units

After moving the points, what is the next step in the process?

• Connect the translated points to form a new line

• Move the points back to their original position

• Erase the original graph

• Change the color of the points

What is the purpose of connecting the translated points?

• To form a new shape

• To create a new line

• To highlight the original points

• To erase the original line

What does the +5 in f(x) + 5 indicate about the direction of movement?

• The graph moves down

• The graph moves left

• The graph moves right

• The graph moves up

What remains unchanged during the translation of the graph?

• The slope of the line

• The x-intercept of the line

• The color of the line

• The y-intercept of the line

What is the equation of the new line after translation?

• 12x - 8

• 12x - 3

• 12x + 8

• 12x + 3

What is the effect of a positive K value in the translation?

• It moves the graph right

• It moves the graph left

• It moves the graph up

• It moves the graph down