Learn Graph Transformations in Mathematics

Warm UP!Name each parent graph… absolute value quadratic linear square root cubic rational

Transformations

Transformations What happens when something transforms? Transformation- a movement or change of a function. • There are three types • Stretch/Shrink • Horizontal/Vertical Shift • Reflections

When we talk about “transformations” we are talking about where the VERTEX is moving! What point does each graph have in common?

Given the following function, If: k > 0, then shift the graph “k” units up If: k < 0, then shift the graph “k” units down Vertical Shifts

Given the following function, Since k > 0, then shift the graph “3” units up

How will the graph look?

Given the following function, We get the expression (x - h) and equal it to zero x - h = 0 x = h If: h> 0, then shift the graph “h” units to the rightIf: h< 0, then shift the graph “h” units to the left Horizontal Shifts

Given the following function, x – 1 = 0 x = 1 Since 1> 0, then shift the graph “1” unit right

Combining vertical & horizontal shifts Example of function that is shifted down 4 units and right 6 units from the original function.

Describe the Transformations

Stretch/Shrink Given the following function, For this equation, a determines how fat or skinny the graph will be. if: |a|>1, then the graph is stretched closer to the y-axis if: |a|=1, then the graph remains the same if: 0<|a|<1, then the graph is shrunk (further from the y-axis)

Reflections • The graph of f(x) is the reflection of the graph of f(x) across the x-axis. • The graph of f(x) is the reflection of the graph of f(x) across the y-axis. How do the following graphs reflect?

Given the following function, Since |5| > 0, then the graph is closer to the y-axis

Given the following function, Since 4 > 0, shift the graph “4” units up x – 1 = 0 x = 1 Since 1> 0, then shift the graph “1” unit to the right Since |5| > 0 shift the graph closer to the y-axis.

Let’s Graph

Congratulations!!You just completed the transformation of ALL FUNCTIONS ARE TRANSFORMED WITH THE SAME PROPERTIES

Name all the transformations:

Write the Equation to this Graph

Write the equation... 3) …of the quadratic equation that has been shifted down 6 units. y = x2 - 6 4) …of the square root function that has been shifted right 25 units and up 2004 units.

Homework • Page 53 # 1 - 15 all • Do NOT graph. • Write what would happen to each graph • Ex: up 1 unit, right 2 units

Learn Graph Transformations in Mathematics