6
4
2
-2
-4
-6
-5 5
r x = -22x-4-2
q x = 0.52x-2
h x = -2x+2-2
g x = 2-x
f x = 2x
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
(MCC9-12.F.IF.7; MCC9-12.F.IF.7e)
Station 1f(x) = 2x
Step 1: Find f(x).
x f(x)
-2-1
0
1
2
Step 2:Plot the coordinates
using the pegs.
Step 3: Connect the pegs using black yarn.
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Station 1f(x) = 2x
Step 1: Find f(x).
x f(x)
-2-1
0
1
2
Step 2:Plot the coordinates
using the pegs.
Step 3: Connect the pegs using black yarn.
¼½124
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Characteristics of f(x)
Domain?
Range?
Horizontal asymptote?
Intervals of increasing?
Intervals of decreasing?
x-intercepts?
y-intercepts?
End behavior?
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Characteristics of f(x)
Domain?
Range?
Horizontal asymptote?
Intervals of increasing?
Intervals of decreasing?
x-intercepts?
y-intercepts?
End behavior?
(-∞, ∞)(0, ∞)y = 0(- ∞, ∞)none(0, 1)Rises on the right
none©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Station 2h(x) = -2(x+2) - 2
Step 1: Find h(x).
x h(x)
0
-1
-2
-3
-4
Step 2:Plot the coordinates
using the pegs.
Step 3: Connect the pegs
using orange yarn.©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Station 2h(x) = -2(x+2) - 2
Step 1: Find h(x).
x h(x)
0
-1
-2
-3
-4
Step 2:Plot the coordinates
using the pegs.
Step 3: Connect the pegs
using orange yarn.
-6-4-3-2½-2¼©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Characteristics of h(x)
Domain?
Range?
Horizontal asymptote?
Intervals of increasing?
Intervals of decreasing?
x-intercepts?
y-intercepts?
End behavior?
Transformations of f(x)
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Characteristics of h(x)
Domain?
Range?
Horizontal asymptote?
Intervals of increasing?
Intervals of decreasing?
x-intercepts?
y-intercepts?
End behavior?
Transformations of f(x)
(-∞, ∞)(-∞, -2)y = -2(- ∞, ∞)none(0, -6)none
Horizontal shift ← 2 unitsVertical shift ↓ 2 unitsReflection across x-axisFalls on the right
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Station 3q(x) = ½(2)(x-2)
Step 1: Find q(x).
x q(x)
1
2
3
4
5
Step 2:Plot the coordinates
using the pegs.
Step 3: Connect the pegs using green yarn.
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Station 3q(x) = ½(2)(x-2)
Step 1: Find q(x).
x q(x)
1
2
3
4
5
Step 2:Plot the coordinates
using the pegs.
Step 3: Connect the pegs using green yarn.
¼½124
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Characteristics of q(x)
Domain?
Range?
Horizontal asymptote?
Intervals of increasing?
Intervals of decreasing?
x-intercepts?
y-intercepts?
End behavior?
Transformations of f(x)
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Characteristics of q(x)
Domain?
Range?
Horizontal asymptote?
Intervals of increasing?
Intervals of decreasing?
x-intercepts?
y-intercepts?
End behavior?
Transformations of f(x)
(-∞, ∞)(0, ∞)y = 0(- ∞, ∞)none(0, 1/8)none
Horizontal shift → 2 unitsVertical compression by a factor of ½Rises on the right
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Station 4r(x) = -2(2)(x-4) - 2
Step 1: Find r(x).
x r(x)
1
2
3
4
5
Step 2:Plot the coordinates
using the pegs.
Step 3: Connect the pegs using purple yarn.
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Station 4r(x) = -2(2)(x-4) - 2
Step 1: Find r(x).
x r(x)
1
2
3
4
5
Step 2:Plot the coordinates
using the pegs.
Step 3: Connect the pegs using purple yarn.
-2¼-2½-3-4-6©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Characteristics of r(x)
Domain?
Range?
Horizontal asymptote?
Intervals of increasing?
Intervals of decreasing?
x-intercepts?
y-intercepts?
End behavior?
Transformations of f(x)
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Characteristics of r(x)
Domain?
Range?
Horizontal asymptote?
Intervals of increasing?
Intervals of decreasing?
x-intercepts?
y-intercepts?
End behavior?
Transformations of f(x)
(-∞, ∞)(-∞, -2)y = -2(- ∞, ∞)none(0, -21/8)none
Horizontal shift → 4 units; Vertical shift ↓ 2 unitsVertical stretch by a factor of 2; Reflection across x-axisFalls on the right
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Station 5g(x) = 2-x
Step 1: Find g(x).
x g(x)
-2
-1
0
1
2
Step 2:Plot the coordinates
using the pegs.
Step 3: Connect the pegs using pink yarn.
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Station 5g(x) = 2-x
Step 1: Find g(x).
x g(x)
-2
-1
0
1
2
Step 2:Plot the coordinates
using the pegs.
Step 3: Connect the pegs using pink yarn.
421½¼
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Characteristics of g(x)
Domain?
Range?
Horizontal asymptote?
Intervals of increasing?
Intervals of decreasing?
x-intercepts?
y-intercepts?
End behavior?
Transformations of f(x)
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Characteristics of g(x)
Domain?
Range?
Horizontal asymptote?
Intervals of increasing?
Intervals of decreasing?
x-intercepts?
y-intercepts?
End behavior?
Transformations of f(x)
(-∞, ∞)(0, ∞)y = 0(- ∞, ∞)none(0, 1)none
Reflection across y-axisRises on the left
©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Characteristics
Domain?
Range?
Horizontal asymptote?
Intervals of increasing?
Intervals of decreasing?
x-intercepts?
y-intercepts?
End behavior?
Transformations
Station #_____
Equation
____________________
Characteristics
Domain?
Range?
Horizontal asymptote?
Intervals of increasing?
Intervals of decreasing?
x-intercepts?
y-intercepts?
End behavior?
Transformations
Station #_____
Equation
____________________