Reflection

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.

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?

Related terms

Exponential Function:

A mathematical function in which an independent variable appears in the exponent. Example: $f(x) = a^x$, where $a > 0$.

Logarithmic Function:

$A mathematical function that is the inverse of an exponential function. Example: $f(x) = \log_b(x)$, where $b > 1$.

Transformation: $An operation that moves or changes a geometric figure or graph in some way to produce a new figure or graph.