Polynomial Functions & Equations
This is just one example of an even function.
What is f(x) = ...
Any x-terms in functions must have an even degree only. May contain a constant term at the end.
Answer must include "f(x) = " (or equivalent) to state that it is a function.
This/these is/are the only trigonometric ratio(s) that does/do not have x-intercepts.
What are sec(x) and csc(x)?
(also acceptable: what are secant and cosecant?)
This/these is/are the exact solution(s) to the following logarithmic equation:
log2x + log2(x + 2) = 3.
What is x = 2?
This/these is/are the equation(s) of the vertical asymptote(s) of the following function:
a(x) = x + 5 / (x2 + 8x + 15)
What is x = -3?
(answer must have "x =..." in front since question asks for the equation of the asymptote)
This is the most simplified form of the following expression:
log(sqrt(x))3 + logx2 - log(sqrt(x))
What is 3logx?
What are (x - 4), (x + 2) and (3x + 1)?
This is the exact value of the following expression:
sin(5pi / 12)*cos(pi/4) + cos(5pi / 12)*sin(pi / 4).
What is (root3 / 2) ?
This/these is/are the exact solution(s) to the following equation:
42x - 4x - 20 = 0.
What is x = log5 / log 4?
These are the domain and range, respectively, of the following function:
h(x) = -1 / (x2 - 6x + 9).
What are (-infinity, 3) and (3, infinity) for the domain and (0, -infinity) for the range?
(also accept set notation: x is an element of the real numbers such that x does not equal 3; y is an element of the real numbers such that y is less than 0).
These trigonometric ratios (both primary and reciprocal) have a vertical asymptote at x = pi/2 and x = 3pi / 2 in the interval [0, 2pi].
What are y = tanx and y = secx?
This is the remainder when the polynomial
-8x4 - 4x + 10x3 - x2 + 15
is divided by 2x - 1.
What is 27/2? (13.5)
This is the exact value for the following expression:
cos(pi/6)csc(pi/3) + sin(pi/4)
What is (2 + root2)/2?
(also acceptable: (root2 + 1)/root2 )
This/these is/are the exact solution(s) to the following equation:
82x+1 = 32x-3
What is x = -18?
This is the equation of the horizontal asymptote of a rational function in the form f(x) = (ax + b)/(cx + d).
What is y = a/c?
Note: answer must have "y = ..." in it since question asks for "equation of the asymptote".
This is the domain and range, respectively, of the following combined function:
y = g(f(x))
where
f(x) = x2 and g(x) = x + 3
What is (-infinity, infinity) and [3, infinity).
(also accept set notation: x is an element of the real numbers; y is an element of the real numbers such that y is greater than or equal to 3).
This is the solution to the following inequality:
-(2x + 3)(x - 1)(3x - 2) <= 0.
What is [-3/2, 2/3] and/or [1, infinity)?
These are all the values of x (rounded to 2 decimal places) in the interval [0, 2pi] such that cscx = 4.
What are 0.25 and 2.89?
This is the domain and range, respectively, of the following function:
y = -log(x - 5) + 2
(also accept set notation: x is an element of the real numbers such that x is greater than 5; y is an element of the real numbers)
This is the equation of the composition function y = g(g(x)), where f(x) = x2 + 3x and g(x) = 2x - 5.
What is y = 4x - 15?
DAILY DOUBLE!
These are the transformations to the x-coordinates of the function y = x4 as it becomes:
y = (1/4)[-2(x-1)]4 + 2
What is:
- reflection over the y-axis
- horizontal compression by factor 1/2
- horizontal/phase shift to the right by 1 unit?
This is the average rate of change of the distance traveled by a boat during the first 10s after leaving shore.
The distance, d, traveled by the boat after t seconds is given by:
d(t) = 0.002t3 + 0.05t2 + 0.3t
What is 1 m/s? (units must be given)
This is the equation used to model the motion of the piston in the following scenario:
"The piston in a lawn mower motor moves up and down 30 times in 1 s. Its total travel from the top position to the bottom position is 10 cm. The vertical position is y, in cm, and time, t, is in seconds. Assume the piston starts from the equilibrium position."
What is y = 5sin(60pi*t)?
(do not accept other equivalent expressions that are off with a phase shift due to the phrase: "Assume the piston starts from the equilibrium position")
This is how long it will take the following investment to double in value:
"A savings bond offers interest at a rate of 6.6%, compounded semi-annually. A $500 bond is purchased."
What is approximately 10.67 years?
This the the profit function, P(n), for the following scenario (where n is the number of cups of cider sold):
"Kathy has a small business selling apple cider at the farmers' market. She pays $35 per day to rent her space at the market, and each cup of cider costs her $1. She sells the cider for $2.50 per cup and brings enough cider and cups to sell a maximum of 200 cups in a day."
What is P(n) = 1.5n - 35?
This is the value of "k" so that x + 3 is a factor of
x3 + 4x2 - 2kx + 3,
What is k = -2?