Reflections of Linear Functions Across Axes
Reflecting linear functions across axes in Algebra 1 (California Reveal Math, Grade 9) produces predictable transformations: reflecting f(x) = mx + b across the x-axis gives -f(x) = -mx - b (both slope and y-intercept change sign), while reflecting across the y-axis gives f(-x) = -mx + b (only the slope changes sign). For example, reflecting f(x) = 2x + 3 across the x-axis gives -2x - 3; across the y-axis gives -2x + 3. Understanding axis reflections is foundational for graphing function transformations in Algebra 1 and Pre-Calculus.
Key Concepts
For a linear function $f(x) = mx + b$:.
Reflection across the x axis: $ f(x) = mx b$ (negate the entire output; slope and y intercept both change sign) Reflection across the y axis: $f( x) = mx + b$ (negate the input; only the slope changes sign).
Common Questions
How do you reflect a linear function across the x-axis?
Negate the entire function output: replace f(x) with -f(x). This changes the sign of both the slope and the y-intercept. For f(x) = 2x + 3, the reflection is -2x - 3.
How do you reflect a linear function across the y-axis?
Replace x with -x in the function: compute f(-x). This only changes the sign of the slope. For f(x) = 2x + 3, the y-axis reflection is f(-x) = -2x + 3.
What changes when a linear function is reflected across the x-axis?
Both the slope and y-intercept change sign. The line flips vertically, mirroring every point across the x-axis.
What changes when a linear function is reflected across the y-axis?
Only the slope changes sign. The y-intercept stays the same. The line flips horizontally, mirroring every point across the y-axis.
Where are reflections of linear functions covered in California Reveal Math Algebra 1?
This topic is taught in California Reveal Math, Algebra 1, as part of Grade 9 function transformations.
How do x-axis and y-axis reflections differ visually?
An x-axis reflection flips the graph upside down. A y-axis reflection flips it left-to-right. For a line, both change the slope's direction but in different ways.
What real-world situation models a reflected linear function?
A profit function could be reflected to model a loss; a temperature increase model could be reflected to model cooling. Reflections represent opposite or inverse scenarios.