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)^3 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 – 3x^2 + 2?
global minimum at x = –1,1; local maximum at x = 0
200
Using interval notation, approximate the intervals where the function f(x) = -x^3 – 2x^2 is increasing and where it is decreasing.
increasing on (-1,0); decreasing on (–∞,-1)U(0, ∞)
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 quadratic function scaled vertically by a factor of 4 and reflected across the y-axis?
f(x) = 4(-x)^2
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) = x^3 +3 x^2 + 1?
local maximum at x = -2; local minimum at x = 0
300
Using interval notation, state the intervals where the function f(x) = (2x – 3)^3 – 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
State the intervals of increasing and decreasing as well as the maximums and minimums.
Inc (-inf, -2) u (0,2)
Dec (-2,0) u (2, inf)
R. Max -2; R. Min 2
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) = (Sq root x ) -3?
f(x) = (x+3)^2
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