Transformations
Inverses
Extrema
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
What are the local extrema of the function f(x) = x^3 – 3x^2 + x + 1?
local maximum at x = 0.18; local minimum at x = 1.8
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
What are the local and global extrema of the function f(x) = x^4 + x^3 – 2x^2 – x + 2?
global minimum at x = –2.4; local minimum at x = 0.4; local maximum at x = –0.25
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
What are the local extrema of the function f(x) = 0.05x^3 – 0.8x^2 + 0.4x + 1?
local maximum at x = 0.26; local minimum at x = 10.4
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
What are the local and global extrema of the function f(x) = 0.04x^4 + 0.2x^3 – 1.9x^2 + 0.1x + 4?
global minimum at x = –7.1; local maximum at x = 0.026; local minimum at x = 3.3
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
What are the local and/or global extrema of the function f(x) = 0.01(x – 5)^4 – 0.1x^3 – 0.4^x + 4?
global minimum at x = 20.1
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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