Domain & Range
Find the domain for the following function:
f(x) = x + 2
Domain: (-∞, ∞)
Solve for x given: |x-3| = 7
x = -4, 10
Given f(x)=2x+3 and g(x)=x2, find (f°g)(x) & (g°f)(x).
(f°g)(x)=2x2+3
(g°f)(x)=(2x+3)2
Find the inverse function for f(x) = 3x-7.
f-1(x) = (x+7)/3
How is this graph being transformed? f(x) = 2(x)-4.
a=2: Vertically stretched by a factor of 2.
b=1: No change.
h=0: No change.
k=-4: Shift down by 4 units.
Who wants a free Yellow Frog!?
+200 points!
Solve for x given: |2x+5|-4=9
x = -9, 4
Who wants a free red frog!?
+100 points!
Who wants a blue frog!?
+400 points!
How is this graph being transformed? t(x)=3(-x+8)
a=3: Vertically stretched by a factor of 3.
b=-1: Reflected across y-axis.
h=-8: Shift left by 8 units.
k=0: No change.
Who wants a free red frog!
+100 points!
Solve for x given: -|(1/5x) + 3| = 6
x = -45, 15
Given f(x)=√(x-1) and g(x)=x2+1, find (f°g)(x) & (g°f)(x).
(f°g)(x) & (g°f)(x) = x
Find the inverse function of f(x) = (2)/(x+1)
f-1(x)=(2/x)+1
Who wants a green frog!?
+300 points!
Find the domain for: √(x + 8).
Domain: [-8, ∞)
Who wants a free green frog!?
+300 points!
Given f(x)=2x and g(x)=x+1, find (f°g)(x) and its domain.
(f°g)(x)= x ÷ (1+2x)
Domain: (-∞, -1/2) U (-1/2, 0) U (0, ∞)
Who wants a yellow frog!?
+200 points!
What are transformations for this graph? After identifying them, come up with 5 coordinate points (start from x=-2 --> x=2) and sketch a graph of what this graph would look like after it undergoes the following transformation(s) for p(x)=-2(1/2x-2)+3
a=-2: Reflect across x-axis, vertically stretched by a factor of 2.
b=1/2: Horizontally stretched by a factor of 2.
h=2: Shift right 2 units.
k=3: Shift up 3 units.
Coordinates: (-2, 7), (0, 5), (2, 3), (4, 1), (6, -1)
Graphs may vary.
Find the domain for: f(x) = 1 ÷ 4 - x.
(-∞, 4) U (4, ∞)
Solve for x given: |-14x+2|≤18, WRITE YOUR FINAL ANSWER IN INEQUALITY NOTATION!!!
-8/7 ≤ x ≤ 10/7
Given f(x)=2x, g(x)=x+1, and h(x)=√x, find:
(f°g°h)(x) and its domain.
(f°g°h)(x)=2√(x)+2
Domain: [0, ∞)
Find the inverse function for f(x)=(2x+1)÷(x-3).
f-1(x)=(3x+1)÷(x-2)
What are the transformations for this graph? After identifying them, come up with 5 coordinate points (start from x=-2 --> x=2) and sketch a graph of what this function would look like after it undergoes the transformations given: 2(-2x+3)2-2.
a=2: Vertically stretched by a factor of 2.
b=-2: Reflect across y-axis; horizontally compressed by a factor of 1/2.
h=-3: Shift left 3 units.
k=-2: Shift down 2 units.
Coordinates: (-2, 2), (-2.5, 0), (-3, -2), (-3.5, 0), (-4, 2)
Graphs may vary.