quiz 2 review
if f(x)= 3x+2, g(x)= x^2 - 4, and h(x)=x-1, find (fogoh)(x)
3x^2-6x-7
if f(x)= 2x^2 - 5x + 3 find f(a+h) - f(a) / h
4a + 2h -5
if f(x)= 2x^2 - 5x + 3 find 2f(a)
4a^2 - 10a + 6
a rectangle has an area of 25 square meters. express the perimeter as a function of the length of a side
50/w + 2w
if f(x)= 2x^2 - 5x + 3 find -f(a)
-2a^2 + 5a - 3
express f(x)= |x-4|/x-4 as a piecewise function
1 if x>4 -1 if x<4
if f(x)= 2x^2 - 5x + 3 find f(-2)
21
if f(x)= 2x^2 - 5x + 3 find f(a+h)
2a^2 + 4ah + 2h^2 - 5a + 5h + 3
if f(x)= 2x^2 - 5x + 3 find f(-a)
2a^2 + 5a + 3
if f(x)= 2x^2 - 5x + 3 find f(a)
2a^2 - 5a + 3
if f(x)= 2x^2 - 5x + 3 find f(a)+h
2a^2 -5a + 3 + h
if f(x) = 3x + 2 find f(a+h)-f(a)/h
3
translation of f(x)= cube root (2x) - 4
(-2,1) (-4,7) (0,7)
find the domain of f(x)=log(3x+5)
(-5/3, infinity)
find the domain of f(x)= 1/3x+4
(-infinity, -4/3) u (-4/3, +infinity)
find the domain of f(x)= (x+5)/x^2-4x+3
(-infinity, 1) u (1,3) u (3, +infinity)
find the domain of f(x)= log (x-2)/x+3
(-inifinity, -3) u (2, infinity)
find the domain of f(x)= sqrt x^2 - 5x - 6
(-inifinty, -1] u [6, inifinity)
find the domain of f(x)= sqrt 3-2x
(-inifinty, 3/2]
decreasing function
(1/5)^x
translation of -2f(3x)+4
(2/3, -4) (0,4) (4/3, 4)
if x=c is a zero of a polynomial function (f(c)=0) then
(x-c) is a factor
if f(x)= 3x+2 & g(x)= x^2 - x -2 find and state the domain of: - (fg)(x) -(f/g)(x)
- 3x^3 - x^2 - 8x - 4, domain: (-infinity, infinity) - 3x+2/x^2 - x -2, domain (-infinity, -1) u (-1,2) u (2, infinty)
if you rent a car for one week and drive 500 miles you will be charged $250. if you drive 800 miles, you will be charged $280 - find the cost function - what is the slope? interpret this value - what is the y-intercept? interpret this value
- m= .1 - slope= .1m (10 cents) is the cost per mile - y-intercept= (0, 200) the base cost to rent the car even if you do not drive it
if f(x)= sqrt x-2 & g(x)= x^2 - x -5 find and state the domain of: - (f+g)(x) -(f-g)(x) -(fg)(x)
- sqrt x-2 + x^2 - x - 5, domain: [2, infinity) - sqrt x-2 - x^2 + x + 5, domain: [2, infinity0 - 50, domain: [2, infinity)
if f(x)= x^2 +2 & g(x)= sqrt x-4 find and state the domain of: - (fog)(x) - (gof)(x) - (fof)(x) - (gog)(x)
- x-2, domain: [4, infinity) - sqrt x^2 - 2, domain: (-infinity, -sqrt 2) u (sqrt 2, infinity) - x^4 + 4x^2 +6, domain: (-infinity, infinity) - 0
if f(x) = x+3 / x+1 find f(x)-f(1)/x-1
-1/x+1
if f(x)= sqrt x find f(x+h)-f(x) / h
1 / sqrt x+h + sqrt x
undefined acts when finding domain
1. vision by zero 2. even roots of negative numbers 3. logs of zero or negative numbers
if f(x)= 2x^2 - 5x + 3 find f(2a)
8a^2 - 10a + 3
a closed rectangular box with a volume of 8 cubic feet has a length that is twice the width. express the height of a box as a function of the width
H(w)= 4/w^2
a box is made from a rectangle that measures 4ft x 5ft by cutting out a square from each side. express the volume of the box as a function of the length of the square
V(x)= x(5-2x)(4-2x)
standard/vertex form of quadratic models
a(x-h)^2 + k
cf(x)
c(y)
f(x)-c
down c units, y-c
determine if f(x)= 4x/x^4 + 2 is even, odd, or neither
even
if f(-x) = f(x) then the function is
even
if f(x)= x^2 + 2 if x<0 -x+1 if x>0 evaluate f(-1), f(1), and f(0) & state the domain & range
f(-1)= 3 f(1)= 0 f(0)= undefined domain: (-infinity, 0) u (0, infinity) range: (-infinity, 1) u (2, infinity)
if f(x)= x+2 if x<0 1-x if x >/= 0 evaluate f(-1), f(1), and f(0) & state the domain & range
f(-1)=1 f(1)=0 f(0)=1 domain: (-infinity, infinity) range: (-infinity,2)
find an example of an increasing function that passes through (3,8)
f(x)= 2^x
rational function
f(x)= 3x + 2/ x^2 -4
quadratic function
f(x)= 3x^2 + 2x - 5
polynomial function
f(x)= 3x^4 - 2x^3 + 8x - 7
exponential function
f(x)= 5^3x+2
increasing function
f(x)= 5^x
general form of quadratic models
f(x)= ax^2 + bx + c
trig function
f(x)= sin(3x+2)
radical function
f(x)= sqrt 3x+2
a quadratic function that has a vertex of (2,1) passes through (3,2)
f(x)=(x-2)^2 +1
if f(3)=f(-2)+f(4)=0 and f(2)=16 find the cubic polynomial function
f(x)=2(x-3)(x+2)(x-4)
linear function
f(x)=3x+2
f(x+c)
left c units, x-c
log function
log(3x+2)
determine if f(x)= 2x^2 - x + 1 is even, odd, or neither
neither
determine is f(x)= 3x/x^2 + 2 is even, odd, or neither
odd
if f(-x)= -f(x0 then the function is
odd
if a function is odd it is symmetric about the
origin
-f(x)
reflection over x-axis, -y
f(-x)
reflection over y-axis, x/-1
f(x-c)
right c units, x+c
express the area of an equilateral triangle as a function of the length of a side
sqrt 3/4 x^2 = A
f(x)+c
up c units, y+c
if f(x)= x^2 - x + 2 find f(x) - f(2) / x-2
x+1
express f(x)= |x+3| as a piecewise function
x+3 if x>/= -3 -x-3 if x<-3
f(cx)
x/c
if a function is even it is symmetric about the
y axis
point-slope form
y-y1=m(x-x1)
find the equation of a line through (3,-2) and (-4,5)
y=-x+1
slope-intercept form
y=mx+b
