Algebra 1A - Transforming Functions

Knowing the relationships between graphs, we could know the relationships between the data being graphed.

7 flashcards · Mathematics · by OctoBlast

1. We have f(x)+k f(x) +k" role="presentation">f(x)+kf(x)+k f(x) +kf(x)+kf(x) +kf(x)+k If 0"> k&gt;0 k &gt; 0" role="presentation">k>0k>0 k > 0k>0k > 0k>0 then the line would go up If k&lt;0 k &lt; 0" role="presentation">k<0k<0 k < 0k<0k < 0k<0 then the line would go down This is called a vertical shift

2. We have f(x+h) f(x+h)" role="presentation">f(x+h)f(x+h) f(x+h)f(x+h)f(x+h)f(x+h) If 0"> h&gt;0 h &gt; 0" role="presentation">h>0h>0 h > 0h>0h > 0h>0 then the line would go to the left If h&lt;0 h&lt;0" role="presentation">h<0h<0 h<0h<0h<0h<0 then the line would go to the right This is called a horizontal shift

3. Moving a function left, right, up, or down is called translation.

4. We have a function f(x) f(x)" role="presentation">f(x)f(x) f(x)f(x)f(x)f(x) If f(x) f(x)" role="presentation">f(x)f(x) f(x)f(x)f(x)f(x) got turned into &#x2212;f(x) -f(x)" role="presentation">−f(x)−f(x) -f(x)−f(x)-f(x)−f(x) then it is an y value change It's a reflection across the x-axis

5. We have a function f(x) f(x)" role="presentation">f(x)f(x) f(x)f(x)f(x)f(x) If f(x) f(x)" role="presentation">f(x)f(x) f(x)f(x)f(x)f(x) got turned into f(&#x2212;x) f(-x)" role="presentation">f(−x)f(−x) f(-x)f(−x)f(-x)f(−x) then it is an x value change Its a reflection across the y-axis

6. The characteristics of a Counterclockwise Rotation: Increase slope Pivot point = y-int

   or y-int stays the same

7. The characteristics of a Clockwise Rotation: Decrease slope Pivot point = y-int

   or y-int stays the same