Transformations of Linear Functions

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More PreCalculus Lessons
Math Worksheets Transformations of linear functions

Learn how to modify the equation of a linear function to shift (translate) the graph up, down, left, or right. Learn how to reflect the graph over an axis. And how to narrow or widen the graph.

Linear Parent Graph and Transformations
Students learn that the linear equation y = x, or the diagonal line that passes through the origin, is called the parent graph for the family of linear equations. Students also learn the different types of transformations of the linear parent graph. For example, if the parent graph is shifted up or down (y = x + 3), the transformation is called a translation. If the parent graph is made steeper or less steep (y = ½ x), the transformation is called a dilation. And if the parent graph is changed so that it falls to the right instead of rising to the right (y = -x), the transformation is called a reflection.

Transforming Linear Functions Part 1

Horizontal shift of |h| units
f(x) → f(x - h)
h > 0 moves right, h < 0 moves left

Vertical shift of |k| units
f(x) → f(x + k)
k > 0 moves up, k < 0 moves down

Reflection across y-axis
f(x) → f(-x)
The lines are symmetric about the y-axis

Reflection across x-axis
f(x) → -f(x)
The lines are symmetric about the x-axis

Stretches and compressions change the slope of a linear function.
If the line becomes steeper, the function has been stretched vertically or compressed horizontally.
If the line becomes flatter, the function has been stretched horizontally or compressed vertically.

Transforming Linear Functions Part.2

Ratio of Surface Areas and Volumes

Scale Factor, Length, Area and Volume for similar shapes
Ratio of lengths = ratio of sides = scale factor
Ratio of surface areas = (ratio of sides)² = (scale factor)²
Ratio of volume = (ratio of sides)³ = (scale factor)³

Similar Figures, Scale Factor, Area & Volume Ratios



Similar Figures, Scale Factor, Area & Volume Ratios



3D Figures - Scale Models and Factors
Learn about scaling 3D figures using scale factor

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