Polynomial and Rational Functions
For the function s(t), s is the number of people swimming at the local pool and t is the temperature of the pool. This is the independent variable of the problem.
What is the temperature of the pool?
This is the range of the function f(x)=log(3-x)+2.
What is all real numbers?
Let f(x)=3x2-4x and g(x)=5-3x. This is the value of f(g(-1)).
What is 160?
No Calculator: This is the value of tan(3π/2).
What is undefined?
The coordinates (3, 2π/3) are this kind of coordinate.
What are polar coordinates?
This is the average rate of change of the function w(r)=√1-4r on the interval -5≤r≤-1.
What is -0.5866?
This is the solution to the equation 4 ⋅ 2x+5-10=22.
What is x=-2?
Let h(x)=(2x-7)4. This is h expressed as a composition of two simpler functions f and g where h(x)=f(g(x)).
What is f(x)=x4 and g(x)=2x-7?
This is the quadrant the terminal ray of 6.6π is located in.
What is quadrant II?
This is (5, 5π/6) converted to rectangular coordinates.
What is (-5√3/2, 5/2)?
This is the end behavior of the function f(x)=5x6-2x3-3.
What is lim f(x)=∞ as x→-∞ and lim f(x)=∞ as x→∞?
Exponential functions either have an exponential growth behavior or an exponential decay behavior. This is the behavior of f(x)=1.4(0.07)x and the reason for that behavior.
What is an exponential decay because 0<b<1?
Let f(x)=1/x-6 and g(x)=1-x. This is the function g ∘ f and the domain of g ∘ f.
What is g(f(x))=1-1/x-6 and the domain R, x≠6?
This is the value of sin(3π/4-5π/6).
What is (√2-√6)/4?
This is (-3, 4) converted to polar coordinates where 0≤0≤2π.
What is (5, 2.241)?
For the polynomial function h(x)=x2-8x+15, this is the interval of x when h(x)≤0.
What is [3, 5]?
The function f is given by f(x)=3log2(x)+8. This is the function f-1(x).
What is f-1(x)=2(x-8/3)?
Given that f(x)=cx-3 and g(x)=cx+5 are both defined on the set of all real numbers and c is a constant, this is the value of (f ∘ g)(x)=(g ∘ f)(x) for all values of x?
What is c=1?
This is 1/1+cot2x written as a single trig identity.
What is sin2x?
This is 10[cos(3π/4)+isin(3π/4)] in rectangular form.
What is -5√2+5i√2?
This is the slant asymptote of the rational function g(x)=(x3-2x2-15x)/(x2+x-6).
What is y=x-3?
In the following, x and y are positive constants. This is log2√(16x3/y2) written as a difference of logarithms.
What is ½(4+3 ⋅ log2x-2log2y)?
Given f(x)=5x-2b while g(x)=4bx, this is the value of g(f(1)) if f(g(1))=36.
What is 8?
This is the inverse of f(x)=2sinx-5 for -π/2≤x≤π/2 and its domain and range.
What is f-1(x)=sin-1(x+5/2) with domain: -7≤x≤-3 and range: -π/2≤y≤π/2?
This is 3+4i in polar form.
What is 5[cos(0.927)+isin(0.927)]?