PRECAL (chapter 1)
sue invested $10,000 part at 5.9% annual interest and the balance at 6.6% annual interest. how much is invested at each rate if a 1-yr interest payment is $634.03?
$3710 at 5.9% and $6290 at 6.6%
find the domain of the given function. f(x)=(x+3)(x-3)/x^2+9)
(-infinity, infinity)
find the range of the function f(x)=8x^5
(-infinity, infinity)
find the domain of the given function. f(x)=x/x-9
(-infinity,9) U (9,infinity)
find the (x,y) pair for the value of the parameter x=3t and y=t^2-9 for t=4
(12,7)
find the domain of the given function. f(x)=sqroot9-x
(infinity,9]
write a mathematical expression for the quantity a salary after a 4.2% increase if the original salary is x dollars
1.042x
one positive number is twice another positive number. the sum of two numbers is 360. find the two numbers
120, 240
anne and nancy use a metal alloy that is 18.25% copper to make jewerlry. how many ounces of a 14% alloy must be mixed with a 21% alloy to form 56 ounces of the desired alloy?
22 ounces
find (fg)(x) and the domain f(x)=7x+7, g(x)=6x^2
42x^3+42x^2; domain: (-infinity, infinity)
write a mathematical expression for the quantity eight less than 5 times a number
5x-8
find the range of the function f(x)=sqroot7+x
[-7, infinity)
a circle is inscribed in a square. write the area of the square as a function of the radius.
a=4r^2
determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain. y=3-x^2
bounded above
write the formula for the function f
f(x)+sqrootx-3
find the inverse of the function f(x)=x^3+4
f^-1(x)=3sqrootx-4
the graph of f(x)=|x| is vertically stretched by a factor of 4.8. this graph is then reflected across the x-axis. finally the graph is shifted 0.3 unites downward.
g(x)=-4.8|x|-0.3
the graph of f(x)=|x^2+6x| is horizontally stretched by a factor of 3
g(x)=|1/3x^2 + 2x|
graph the piecewise-defined function. y(x)={9x+8, if x<0} {2x^2-2, if x>=0}
graph on calculator
describe how to transform the graph of f into the graph of g f(x)=sqrootx and g(x)=sqroot0.2x
horizontally stretch graph of f(x) by a factor of 5
determine the intervals on which the function is increasing, decreasing and constant (there is a graph)
increasing on (-1,infinity); decreasing on (-infinity,-1)
identify intervals on which the function is increasing, decreasing or constant. f(x)=0.5(x+4)^2-8
increasing: (-4, infinity) decreasing: (-infinity, -4)
graph the function and determine if it has a point of discontinuity at x=0. if there is a discontinuity, tell whether it is removable or non-removable. g(x)=x^2+6x/x
linear, passing through 6; yes, removable
estimate graphically the local maximum and minimum of f(x)=1/3x^3+x^2-3x
local maximum: 9; local minimum: -1.67
tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown
look at graph
determine if the function is one-to-one
no
determine whether the function is even, odd or neither. f(x)=-7x^5-7x^3
odd
describe how the graph of y=x^2 can be transformed y=(x+9)^2-3
shift the graph of y=x^2 left 9 units, then down 3 units
describe how the graph of y=x^2 can be transformed y=(x-19)^2
shift the graph of y=x^2 right 19 units
describe how the graph of y=x^2 can be transformed y=x^2+3
shift the graph y=x^2 up 3 units
find (f+g)(x) and the domain f(x)=sqroot3x+7, g(x)=sqroot3x-7
sqroot3x+7 + sqroot3x-7 domain: [7/3, infinity)
determine whether the graph is the graph of a function.
straight line test
identify which of the twelve functions below fit the description given. y=x, y=x^2, y=x^3, y=|x|, y=1/x, y=e^x, y=sqrootx, y=lnx, y=sinx, y=cosx, y=int(x), y=1/1+e^-x)
the three functions that are even: y=x^2, y=cosx, y=|x|
match the equation with the graph
use calculator
find the asymptotes of the given function. g(x)=x-6/(x-1)(x+3) vertical asymptotes
x=-3 x=1
graph the inverse of the function plotted. use a dashed curve for the inverse
y=x, graph moves down