Transformations
What is an equation for a quadratic function shifted up by 2?
f(x) = x2 + 2
Given that f(x) = x2 - 3 and g(x) = 2x + 1, find (f + g)(x).
x2 + 2x - 2
Using interval notation, state the intervals where the function f(x) = (2x – 3)2 is increasing
(1.5, ∞)
If f(x) = x2 and g(x) = x – 2, what is the equation for f(g(x))?
f(g(x)) = (x – 2)2
Find the variation constant if y varies inversely as x and y = 1/5 when x = 35
k = 7
What is an equation for the absolute value function shifted to the left by 20?
f(x) = |x + 20|
Given that f(x) = x2 - 3 and g(x) = 2x + 1, find (f - g)(-1).
-1
Using interval notation, state the intervals where the function f(x) = (2x – 3)2 is decreasing.
decreasing on (–∞,1.5)
If f(x) = x2 and g(x) = x – 2, what is the equation for g(f(x))?
g(f(x)) = x2 – 2
Find the variation constant if y varies directly as x and y = 0.9 when x = 0.4
k = 2.25
What is an equation for a quadratic equation with a vertical stretch of 2 and a horizontal shift right 3?
f(x) = 2(x - 3)2
Given that
f(x) = sqrt (x+3)
and g(x) = 2x + 1, find the domain of (f + g)(x).
(-3, oo)
Using interval notation, state the intervals where the function f(x) = -(x – 3)2 + 3 is increasing and where it is decreasing.
increasing on (–∞, 3) decreasing (3, ∞)
If f(x) = 2x2 – x and g(x) = x – 5, what is the equation for f(g(x))?
f(g(x)) = 2(x – 5)2 – (x – 5)
Find the equation for: y varies directly as the square of x and y = 6 when x = 3
y = 2/3x^2
What kind of transformation is the result of f(x) --> f(-x)?
reflection across y-axis
Given that
f(x) = sqrt (x + 6) and g(x) = 1/x find the domain of
f(x)/g(x)
x != 0
Symmetric with respect to the origin
Find f(x) and g(x) such that f(g(x))=h(x) where
h(x)= 3x2
g(x)= x2
f(x)=3x
Find the equation for y varies jointly as x and z and inversely as the square of w, and
y = 12/5, x = 16, z = 3, and w = 5
(5xz)/(4w^2)
What is an equation for a cubic function shifted up by 5, to the right by 4, and reflected across the x-axis?
f(x) = – [(x – 4)3 + 5]
Rick's lumberyard has 480 yd of fencing with which to enclose a rectangular area. If the enclosed area is x yards long, express its area as a function of length.
A(x) = x(240 - x)
Is the function f(x) = 5x7 -6x3 - 2x even, odd, or neither?
odd
What is the domain of f(g(x)) if
f(x) = 1/(3+x)
and g(x) = x + 4
x != -7
The weight M of an object on Mars varies directly as its weight E on Earth. A person who weighs 95 lbs on Earth weighs 35.9 lbs on Mars. How much would a 100 lb person weigh on Mars?
37.8 lbs