Reflection Linear Functions Example

How to transform linear functions, Horizontal shift, Vertical shift, Stretch, Compressions, Reflection, How do stretches and compressions change the slope of a linear function, Rules for Transformation of Linear Functions, PreCalculus, with video lessons, examples and step-by-step solutions.

Section 7.2 Rotations, reflections, projections and dilations Subsection 7.2.1 Transformations 92T92colon 92R292to92R292 We wish to consider some transformations that are geometrically inspired. The following examples from 9292R292 will be useful as we study linear transformations. Example 7.2.1. A rotation in the plane.

Another transformation that can be applied to a function is a reflection over the latexxlatex- or latexylatex-axis. A vertical reflection reflects a graph vertically across the latexxlatex-axis, while a horizontal reflection reflects a graph horizontally across the latexylatex-axis. The reflections are shown in Figure 9.

Flipping a function upside-down always works this way you slap a quotminusquot on the whole thing. The quotflipping upside-downquot thing is, slightly more technically, a quotmirroringquot of the original graph in the x-axis.If you think of taking a mirror and resting it vertically on the x-axis, you'd see a portion of the original graph upside-down in the mirror.

Hence, we classify reflections of the function as Reflection of a function over x - axis or vertical reflection Reflection of a function over y- axis or horizontal reflection Reflection of a function over x and y axis All these types of reflections can be used for reflecting linear functions and non-linear functions.

For example, all linear functions form a family because all of their graphs are the same basic shape. A parent function is the most basic function in a family. For linear functions, the parent function is fx x. Reflection of a Linear Function. When the slope m is multiplied by -1 in fx mx b, the graph is reflected across the y-axis.

here are the domains of the functions in Example 4. Domain of Domain of Domain of k x x 2 x 2 h x x x 0 g x x x 0 Example 4 Reflections and Shifts Compare the graph of each function with the graph of a. b. c.g x x h x x k x x 2 f x x. Algebraic Solution a. Relative to the graph of the graph of is a reflection in the -axis because b.

A reflection of a function is just the image of the curve with respect to either x-axis or y-axis. This occurs whenever we see the multiplication of a minus sign happening somewhere in the function. Here, y - fx is the reflection of y fx with respect to the x-axis. y f-x is the reflection of y fx with resepct to the y-axis.

All other linear functions can be created by using a transformation translation, reflection, and stretching on the parent function fx x. The notation for transformation is to rename the

Example 3 Finding the Equation of a Function When Given the Graph of Its Reflection in an Axis. The following linear graph represents a function after a reflection in the -axis. Find the original function .