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