Transformations
Inverses
Decomposition
Incr. & Decr.
Composition
100
What is an equation for the squaring function shifted up by 2?
f(x) = x^2 + 2
100
What is an equation for the inverse of the function f(x) = 5x?
f(x) = x/5
100

Find f(x) and g(x) such that f(g(x))=h(x) where

h(x)= 3x2

g(x)= x2

f(x)=3x

100
Using interval notation, state the intervals where the function f(x) = (2x – 3)^2 is increasing and where it is decreasing.
decreasing on (–∞,1.5)U(1.5, ∞)
100
If f(x) = x^2 and g(x) = x – 2, what is the equation for f(g(x))?
f(g(x)) = (x – 2)^2
200
What is an equation for the absolute value function shifted to the left by 20?
f(x) = |x + 20|
200
What is the equation for the inverse of the function f(x) = 7x + 1?
f(x) = (x – 1)/7
200

Find f(x) and g(x) such that f(g(x))=h(x) where

h(x)= (3x)2

g(x)=3x

f(x)=x2

200
Using interval notation, state the intervals where the function f(x) = (2x – 3)^2 – x^2 is increasing and where it is decreasing.
decreasing on (1.19,1.90); increasing on (–∞,1.19)U(1.90, ∞)
200
If f(x) = x^2 and g(x) = x – 2, what is the equation for g(f(x))?
g(f(x)) = x^2 – 2
300
What is an equation for the exponential function scaled vertically by a factor of 4 and reflected across the y-axis?
f(x) = 4^(e–x)
300
What is the equation for the inverse of the function f(x) = x/2 + 15?
f(x) = 2(x – 15)
300

Find f(x) and g(x) such that f(g(x))=h(x) where

h(x)= 5+x2

g(x)=x2

f(x)=5+x

300
Using interval notation, state the intervals where the function f(x) = (2x – 3)^2 – x^2 is increasing and where it is decreasing.
decreasing on (1.19,1.90); increasing on (–∞,1.19)U(1.90, ∞)
300
If f(x) = 2x^2 – x and g(x) = x – 5, what is the equation for f(g(x))?
f(g(x)) = 2(x – 5)^2 – (x – 5)
400
What is an equation for the cubing function shifted up by 5, to the right by 4, and reflected across the x-axis?
f(x) = – [(x – 4)^3 + 5]
400
What is the equation for the inverse of the function f(x) = 2 – 3x?
f(x) = (x – 2)/ –3
400

Find f(x) and g(x) such that f(g(x))=h(x) where

h(x)=3x4+x2

g(x)=x2

f(x)=3x2 + x

400
Using interval notation, state the intervals where the function f(x) = 0.6x4 + 1.8x^3 + x^2 – x + 1 is increasing and where it is decreasing.
decreasing on (–∞,1.52)U(–1, 0.27); increasing on (–1.52, –1)U(0.27, ∞)
400
If f(x) = 2x^2 – x and g(x) = x – 5, what is the equation for g(f(x))?
g(f(x)) = 2x^2 – x – 5
500
What is an equation for the function f(x) = 3x – 2 after it is reflected across the y = x line?
f(x) = (x + 2)/3
500
What is the equation for the inverse of the function f(x) = ex – 8?
f(x) = log(x + 8)
500

Find f(x) and g(x) such that f(g(x))=h(x) where

h(x)=6w8 - 5w2

g(x)=w2

f(x)=6w4 - 5w

500
Bonus, you get this one for free!
Free
500
If f(x) = 2x^2 – x, g(x) = x – 5, and h(x) = x/3, what is the equation for h(g(f(x)))?
h(g(f(x))) = (2x2 – x – 5)/3
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