Graphs of Equations
Find the midpoint of the line segment with endpoints (6, -2) and (4, -3).
(5, -5/2)
Find f(t+1) for f(x) = x^2 + 1
f(t+1) = t^2 + 2t + 2
Find the slope and y-intercept of the line.
2x-3y = 6
y = 2/3*x-2
slope: 2/3
y-int: (0,-2)
Find f+g, f-g, and fg for
f(x) = x^2-4 and g(x) = sqrt(3-x)
What is the domain for each?
f+g(x) = x^2 - 4 + sqrt(3-x)
f-g(x) = x^2 - 4 - sqrt(3-x)
fg(x) = (x^2-4)sqrt(3-x)
Domain: (-infty, 3]
Find the intercepts of the following equation:
y = x^2 - 12
y int: (0, -12)
x int (2sqrt(3),0) (-2sqrt(3),0)
Find the distance between the points
(6, -2) and (4, -3).
sqrt(5)
Find the domain of f(x) = sqrt(25-x^2).
[-5,5]
Find the slope of the line passing through the points (5, -2) and (-1,4).
m = (4+2)/(-1-5) = 6/-6 = -1
Find f/g(x) for f(x) = x^2-4, g(x) = sqrt(3-x).
What is the domain of f/g?
f/g(x) = (x^2-4)/sqrt(3-x)
(-infty,3)
Find a mathematical model that represents the statement:
"v varies directly as the square root of s"
v = k*sqrt(s)
Find the x and y intercepts for the following equation:
y = (x-3)^2 - 4
y-int: (0, 5)
x-ints: (5,0), (1, 0)
Find the average rate of change of
f(x) = -x^2 + 8x - 4
from x1 = 0 to x2 = 4.
4
Find the slope-intercept form of the line passing through (6, -5) with slope m = 1/3.
y + 5 = 1/3(x-6)
y = 1/3*x - 7
Find the inverse for the function (if possible)
f(x) = (x-4)/5
f^-1= 5x+4
Find the mathematical model that represents the statement:
b varies inversely as a, and b = 32 when a = 1.5
b = 48/a
Test for symmetry:
y = -6 - x^3
No symmetry.
Identify the parent function f then describe the sequence of transformations from f to h.
h(x) = 1/2(x-1)^2 - 2
f(x) = x^2
Horizontal shift one unit left. Vertical compression by a factor of 1/2. Vertical shift 2 units down.
Find the slope-intercept equation of the line parallel to the line 5x-4y=8 passing through the point ( 3, -2).
y = 5/4*x - 23/4
Find f(g(x)) for f(x) = x^2-4 and g(x) = sqrt(3-x).
(Daily Double Bonus)
f(g(x)) = -x-1
The cost of constructing a wooden box with a square base varies jointly as the height of the box and the square of the width of the box. Constructing a box of height 16cm and a width of 6cm costs $28.80. How much would it cost to construct a box of height 14 cm and of width 8 cm?
$44.80
Write the standard form of the equation of the circle for which the endpoints of a diameter are (0, 0) and (4,6).
Center (2, 3), radius: sqrt(13)
(x-2)^2 + (y-3)^2= 13
Is the following function even, odd, or neither?
f(x) = 2x*sqrt(x^2+3)
Odd.
Find the equation of the line perpendicular to the line 2x + 3y = 5 passing through the point (-8,3).
y = 3/2*x +15
A company manufactures bronze widgets. Each widget costs $3.50 in raw materials and it costs the company $3,000 (one time only) to set up a production run.
If the demand function for widgets is D(x) = 9 - 0.01x, write the profit function.
3000+9x-0.01x^2
What can be said about the product of each pair of functions?
a) Two even functions
b) Two odd functions
c) An odd function and an even function
a) Even
b) Even
c) Odd