study guides for every class

that actually explain what's on your next test

Reflection

from class:

College Algebra

Definition

Reflection is a transformation that flips a graph over a specified axis, creating a mirror image. In algebra, this often involves reflecting exponential and logarithmic functions over the x-axis or y-axis.

congrats on reading the definition of reflection. now let's actually learn it.

ok, let's learn stuff

5 Must Know Facts For Your Next Test

  1. Reflecting an exponential function $y = a^x$ over the x-axis results in $y = -a^x$.
  2. Reflecting a logarithmic function $y = \log_b(x)$ over the y-axis results in $y = \log_b(-x)$.
  3. Reflections do not change the shape of the graph but they do change its orientation.
  4. When reflecting graphs, key points such as intercepts and asymptotes are also reflected.
  5. The domain and range of functions can be affected by reflections, particularly when involving logarithmic functions.

Review Questions

  • What is the result of reflecting the exponential function $y = e^x$ over the x-axis?
  • How does reflecting the logarithmic function $y = \ln(x)$ over the y-axis affect its graph?
  • If you reflect an exponential function across both axes, what will be its new equation?

"Reflection" also found in:

Subjects (137)

© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.