Lines
What is the y-intercept of y=3x+5?
(0,5)
Does f(x) = -4x2 + 3x - 2 have a maximum, minimum, or neither?
Maximum
k(x) = -2x + 1
Evaluate k(2)-3
What is the end behavior of
f(x) = 5x7 + 2x4 - 2x3 + 3x - 1?
f(x) goes to -∞ as x goes to -∞
f(x) goes to ∞ as x goes to ∞
The average water level in a retention pond is 210 cm. During times of drought, the water level decreases at a rate of 8 cm/day.
Give a linear function W that represents the water level W(t) in cm t days after the drought begins.
W(t) = 210 - 8t
What is the slope of the line given by -6x + 3y = 5?
2
Find the roots of f(x) = x2 + 7x + 12
x = -3, -4
f(x) = x3 - 2x + 1
g(x) = 4x - 1
What is (f+g)(3)?
33
What is the y-intercept of g(x) = 2x4 - 5x2 + x + 11?
(0, 11)
Fahrenheit temperature F is a linear function of Celsius temperature C. The freezing
point of water is 0°C or 32°F, and the boiling point of water is 100°C or 212°F.
What is the linear function F(C)?
F(C) = 1.8C + 32
Equation given point and slope
What is the equation of the line with slope -3 that passes through the point (2, 1)?
y - 1 = -3(x - 2) or
y = -3x + 7
Find the vertex of w(x) = 4x2 + 4x - 2
(Give the x- and y- coordinates)
(-1/2, -3)
Where is this piecewise function increasing, decreasing, and constant?
Increasing: (-∞, -1), (0, 1)
Decreasing: (-1, 0)
Constant: (1, ∞)
Does p(x) = -2x3 + 4x2 - x + 5 have a root in on the interval [2, 3]?
Yes
A lawn service company charges $60 for each call. They have to spend $650 per month on maintenance and advertising. Each lawn costs $36 for labor and gas.
Write the linear function P(x) representing their monthly profit.
P(x) = 24x - 650
What is the equation of the line that passes through the point (-4, 5) and is parallel to 4x - 8y = 10?
y = 1/2x + 7 or
y - 5 = 1/2(x + 4)
Find the roots of h(x) = 3x2 - 5x - 3
(5 + √61)/6
(5 - √61)/6
f(x) = x3 - 2x + 1
g(x) = 4x - 1
What is (g(f(3))?
87
Find roots and multiplicities of v(x) = x3 - 4x2 + 4x
x = 0: multiplicity 1
x = 2: multiplicity 2
A long jumper leaves the ground at an angle of 20° at a speed of 11 m/s. The height of the jumper can be modeled by h(x) = -0.046x2 + 0.364x, where h is the jumper's height in meters, and x is the horizontal distance from the start point.
What is the jumper's maximum height? (round to 2 decimal places)
0.72 m
What is the equation of the line that passes through the points (-2, 6) and (3, -1)?
y - 6 = -7/5(x + 2) or
y + 1 = -7/5(x - 3) or
y = -7/5x +16/5
Find the roots of q(x) = 3x4 - 14x2 + 8
2, -2, √(2/3), -√(2/3)
r(x) = x/(x2-4)
s(x) = √(3x+1)
What is the domain of r(s(x))?
[-1/3, 1) U (1,∞)
This is a graph of f(x). The leading coefficient of f is 1, and the degree of f is 4. What is f(x)?
f(x) = (x-2)2(x+3)(x+1)
The sum of two positive numbers is 20. What two numbers will maximize the product?
10 and 10