Combinations
Compositions
Variation
Inverse
Grab Bag
100
f(x)=6x+12 g(x)=4x+8 What is f(x)+g(x)?
10x+20
100
f(x)=1-x g(x)=1/x^2 What is (g◦f)(x)?
1/(1-x)^2
100
P varies directly as t. If t=5, then P=120. Find the constant of proportionality and then express the statement as a formula.
P=24t
100
f(x)=4-9x Find the inverse
(x-4)/-9
100
f(x)=|2x-3| g(x)=3x-1 Evaluate (f+g)(-2)
0
200
f(x)=√(2x-3) g(x)=√(2x+3) What is f(x)*g(x)?
√(4x^2-9)
200
g(x)=4x+18 h(x)=√(x+2) What is h[3*g(x-2)]?
2*√(3x+8) D: x≥-8/3
200
A varies directly as the cube of B. If B=2, then A=56. Find the constant of proportionality and then express the statement as a formula. Find the value of A when B=1.
A=7B^3 A=7
200
b(x)=√(7-x) Find the inverse
-x^2+7 D: x≤7
200
f(x)=5(9x-5)^2+3(9x-5)+1 Determine functions g and h so that f(x)=g(h(x))
Multiple Answers h(x)=9x-5 g(x)=5x^2+3x+1
300
j(x)=5-x^2+x p(x)=x^2+4x-5 What is p(x)-j(x)?
2x^2+3x-10
300
x f(x) 1 3 2 4 3 1 4 5 5 2 x g(x) 1 3 2 4 3 1 4 5 5 2 x f(g(x)) 1 ? 2 ? 3 ? 4 ? 5 ?
x f(g(x)) 1 10 2 8 3 6 4 2 5 9
300
The intensity of light varies inversely as the square of the distance. If the light intensity is 216-foot candles at 6 feet, find the light intensity at 17 feet.
I=7776/d^2 I~26.9
300
x g(x) 1 3 2 4 3 1 4 5 5 2 x g^-1(x) 1 ? 2 ? 3 ? 4 ? 5 ?
x g^-1(x) 1 3 2 5 3 1 4 2 5 4
300
Varify that these are inverses r(x)=(x-1)/(3x+5) p(x)=(5x+1)/(1-3x)
p(r(x))=x r(p(x))=x
400
b(x)=5x+2 v(x)=8x+11 What is v(x)/b(x)? *Don't forget to state the domain*
(8x+11)/(5x+2) x≠-2/5
400
d(x)=x^2+9 y(x)=√(x^2+x-6) What is (d◦y)(x)?
x^2+x-3 D: x≤-3 or x≥2
400
The strenth of a rectangular beam varies jointly as its width and the square of its depth if the strength of a beam 2 inches wide by 10 inches deep is 1000 pounds per square inch, what is the strength of a beam 5 inches wide and 10 inches deep?
2500 pounds per square inch
400
r(x)= (6x-5)/(2x+9) Find the inverse
(9x+5)/(6-2x) D: x≠1/3
400
Use your calculator to determine the equation of the least-squares regression line that models the relationship between x and y. Write this equation x g(x) 1 80 3 71 7 52 10 43 15 27
y=-3.8+81.9
500
q(x)=24x^3+75 r(x)=√(x^2-9) What is q(x)/r(x)? *State the domain*
(24x^3+75)/(√(x^2-9)) x>3 or x<-3
500
w(x)=(x+9)/(5x+3) i(x)=(7x-2)/(x-4) What is (w◦i)(x)?
(8x-19)/(19x-11) D: x≠4,11/19
500
C varies directly with x and inversely with the square root of w. If x=3 and w=81, then C=5. Find the constant of proportionality and then express the statement as a formula. Find the value of C when x=6 and w=225.
C=6
500
Restrict the domain of the function to make it one-to-one and then find the inverse. Give the domain and range for both the original functions and the inverse function. f(x)=(x-5)^2+3
f(x) D: x≥5 R: y≥3 f^-1(x)=√(x-3)+5 D: x≥3 R: y≥5
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