Review

Combinations

100

f(x)=6x+12 g(x)=4x+8 What is f(x)+g(x)?

10x+20

200

f(x)=√(2x-3) g(x)=√(2x+3) What is f(x)*g(x)?

√(4x^2-9)

300

j(x)=5-x^2+x p(x)=x^2+4x-5 What is p(x)-j(x)?

2x^2+3x-10

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

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

Compositions

100

f(x)=1-x g(x)=1/x^2 What is (g◦f)(x)?

1/(1-x)^2

200

g(x)=4x+18 h(x)=√(x+2) What is h[3*g(x-2)]?

2*√(3x+8) D: x≥-8/3

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

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

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

Variation

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

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

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

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

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

Inverse

100

f(x)=4-9x Find the inverse

(x-4)/-9

200

b(x)=√(7-x) Find the inverse

-x^2+7 D: x≤7

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

400

r(x)= (6x-5)/(2x+9) Find the inverse

(9x+5)/(6-2x) D: x≠1/3

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

Grab Bag

100

f(x)=|2x-3| g(x)=3x-1 Evaluate (f+g)(-2)

0

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

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

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