1. MAT 150 Algebra Class #12 Topics: Transformations of Graphs of Functions Symmetric about the y- axis, x-axis or origin Is a function odd, even or neither?

2. Parent Functions FunctionIdentifySketch Linear Quadratic Square Root Rational Power Logarithm Absolute Value Cubic

3. Transformation of Graphs of Functions Type of ShiftMathematical Language Verbal Language Vertical Shiftsy = f(x) + kGraph is shifted k units up if k > 0 and k units down if k< 0 Horizontal Shiftsy = f(x – h)Graph is shifted h units right if h > 0 and h units left if h < 0. Stretchingy = a* f(x)Graph is vertically stretched using a factor of |a| if |a|> 1.

4. Transformation of Graphs of Functions Type of ShiftMathematical Language Verbal Language Compressingy = a* f(x)Graph is vertically stretched using a factor of |a| if |a|< 1. Reflections x-axis y = -f(x)Graph is reflected across the x-axis. Reflection y-axisY = f(-x)Graph is reflected across the y-axis.

5. Example

6. Symmetry Mathematical Language Verbal Language Respect to y-axisf(-x) = f(x)If every point (x, y) on the graph, the point (-x, y) is also on the graph. Such a function is called an EVEN FUNCTION. Respect to the originf(-x) = -f(x)If every point (x, y) on the graph, the point (-x, -y) is also on the graph. Such a function is called an ODD FUNCTION. Respect to x-axisIf every point (x, y) on the graph, the point (x, - y) is also on the graph.

7. Examples

8. Assignment Pg. 259 #3-9odd #17-18 #23 & 25 #27-35 odd #51, 60