.2A Stretches 1. The graph of y + 3 = f(x) is the graph of f(x) translated… up 3 units left 3 units down 3 units right 3 units 2. The graph of f(x) + 4 is the graph of f(x) translated… 4 units up 4 units left 4 units down 4 units right 3. The graph of f(x – 7) + 6 is the graph of f(x) that has been translated.. 7 units left, 6 units up 7 units left, 6 units down 7 units right, 6 units down 7 units right, 6 units up 4. In general, the graph of f(x – h) + k, where h and k are positive, as compared to the parent function graph f(x), is translated h units left and k units up h units right and k units up x x x x Math 30-1 1
1.2A Stretches. The graph of y + 3 = f(x) is the graph of f ( x ) translated … up 3 units left 3 units down 3 units right 3 units. x. 2. The graph of f(x) + 4 is the graph of f ( x ) translated … - PowerPoint PPT Presentation
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Math 30-1 1
1.2A Stretches1. The graph of y + 3 = f(x) is the graph of f(x) translated…
up 3 units left 3 units down 3 units right 3 units
2. The graph of f(x) + 4 is the graph of f(x) translated…
4 units up 4 units left 4 units down 4 units right
3. The graph of f(x – 7) + 6 is the graph of f(x) that has been translated..
7 units left, 6 units up 7 units left, 6 units down
7 units right, 6 units down 7 units right, 6 units up
4. In general, the graph of f(x – h) + k, where h and k are positive, as compared to the parent function graph f(x), is translated
h units left and k units up h units right and k units up h units left and k units down h units right and k units down
x
x
x
x
Math 30-1 2
5. When the output of a function y = f(x) is multiplied by -1, the result, y = -f(x), is a reflection of the graph in the a. x – axisb. y – axisc. line y = x.
6. When y = f(x) is transformed to y = f(-x), then (x, y) is transformed to d. (-x, -y)e. (x , -y)f. (-x, y)
Math 30-1 3
Function Transformations: Vertical Stretch
1.2A Vertical Stretches
Vertical Stretches: The effect of parameter a. ( )y af xA stretch changes the shape of the graph. (Translations changed the position of a graph.)
( )y af x|a| describes a vertical stretch about the x-axis.
An Invariant point is a point on a graph that remains unchanged after a transformation.
Math 30-1 4
In general, for any function y = f(x), the graph of the function y =a f(x) has been vertically stretched about the x-axis by a factor of |a| .
The point (x, y) → (x, ay). Only the y coordinates are affected.
Vertical Stretches
Invariant points are on the line of stretch, the x-axis. are the x-intercepts.
When |a| > 1, the points on the graph move farther away from the x-axis.
When |a|< 1, the points on the graph move closer to the x-axis.