Transformations
What is an equation for the quadratic function shifted up by 2?
f(x) = x^2 + 2
What is an equation for the inverse of the function f(x) = 5x ?
f(x) = x/5
Find f(x) and g(x) such that f(g(x))=h(x) where
h(x)= 3x2
g(x)= x2
f(x)=3x
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)uu(1.5, ∞)
If
f(x) = x^2 and g(x) = x – 2
what is the equation for f(g(x))?
f(g(x)) = (x – 2)^2
What is the equation for the inverse of the function
f(x) = 7x + 1
f(x) = (x – 1)/7
Find f(x) and g(x) such that f(g(x))=h(x) where
h(x)= (3x)2
g(x)=3x
f(x)=x2
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)uu(1.90, ∞)
If
f(x) = x^2 and g(x) = x – 2
what is the equation for g(f(x))?
g(f(x)) = x^2 – 2
What is an equation for the reciprocal function expanded vertically by a factor of 4 and reflected across the y-axis?
f(x) = 4(1/-x)
What is the equation for the inverse of the function
f(x) = x/2 + 15
f(x) = 2(x – 15)
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
Using interval notation, state the intervals where the function
f(x) = (2x – 3)^3 + 5
is increasing and where it is decreasing.
increasing on
(–∞,1.044)uu(1.044, ∞)
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)
What is an equation for the cubic function shifted up by 5, to the right by 4, and reflected across the x-axis?
f(x) = – [(x – 4)^3 + 5]
What is the equation for the inverse of the function
f(x) = sqrt(2 – 3x)
f(x) = (x^2 – 2)/ (–3)
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
Using interval notation, state the intervals where the function
f(x)=0.6x^{4}+1.8x^{3}+x^{2}-x+1
is increasing and where it is decreasing.
decreasing on
(–∞,-1.52)uu(–1, 0.27)
; increasing on
(–1.52, –1)uu(0.27, ∞)
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
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
What is the equation for the inverse of the function
(x-1)^3 +sqrt(18)
f(x)=root(3)(x-sqrt(18))+1
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
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))) = (2x^2 – x – 5)/3