Intro to Functions
Polynomial Functions
Rational Functions
Exponentials and Logarithms
Systems, Matrices & Graphs
100
A function has this if the function is one-to-one.
What is an inverse?
100
This is all the possible rational zeros of the polynomial:
p(x)=x^4+3x^3-3x^2-7x+6
What is
\pm 1, \pm2, \pm3, \pm6?
100
This is the domain of the following rational function:
f(x)=frac{x+2}{x^2-81}
What is
(-\infty, -9)\cup(-9,9)\cup(9,\infty)?
100
This is the property that can be invoked if two exponents are equal to each other and have the same bases.
What is like-bases OR one-to-one property?
100
This is a unique matrix of the following form for a consistent independent solution:
[[1,0,0,7],[0,1,0,-2],[0,0,1,3]]
What is reduced row echelon form or RREF?
200
This is the function that is even, possesses the domain of
(-\infty,0)\cup(0,\infty)
and behaves as the graph:
What is
f(x)=1/x^2
or the squared reciprocal function?
200
These are the roots/zeroes of the following function:
f(x)=(4x-1)^2-2(4x-1)+1
What is
x=1/2?
200
This is the horizontal asymptote of the following function:
f(x)=\frac{4}{x+3}
What is
y=0?
200
This is the equation
5^x=125
in logarithmic form.
What is
log_5 125 = x?
200
These are the valid operations for solving a matrix:
What are adding two rows, switching two rows, and multiplying a row by a scalar?
300
This is the general formula of the transformation form of a function.
What is
y=Af(B(x-h))+k?
300
This is the constant of the following polynomial function:
f(x)=2(x+1)^2(6x-3)(x+2)^2
What is -24?
300
This is the coordinate of the holes for the following function:
g(x)=\frac{x^2-4}{x^2-x-6}
What is
(-2,\frac{4}{5})?
300
This is the value of the following expression:
log_5(-2)
What is undefined?
300
This is the augmented matrix for the following functions:
{(2x+y=3),(-3y+z=-5),(3x-10z=4):}
What is
[[2,1,0,3],[0,-3,1,-5],[3,0,-10,4]]
400
The inverse for the function:
f(x)=-root(3)(x+1)+2
What is
f^-1(x)=(2-x)^3-1?
400
This is the factored form of the polynomial function, given that f(1) = 0:
f(x)=x^3-x^2+4x-4
What is
f(x)=(x^2+4)(x-1)?
400
This is the equation that describes the following rational function r(x):
- Vertical asymptote at x = -5
- Graph bounces on the x-axis at x = 2
- y-int at (0,4)
What is
r(x)=\frac{5(x-2)^2}{x+5}?
400
This is the value of x for the following exponential equation:
27^x=81
What is
x = 4/3?
400
This is the graph of the following polynomial function:
f(x)=-4x(x-2)(x+1)^2(x+3)
What is
500
The domain of the following function:
g(x)=(\sqrt(4x-2))/(x^2-16)
What is
[1/2,4)\cup(4,\infty)?
500
This is the factored form of the following functions with linear factors (x-1) and (x-2):
h(x)=x^4-2x^3-7x^2+20x-12
What is
f(x)=(x-2)^2(x-1)(x+3)?
500
This is the end behavior for the following function
f(x)=\frac{5-7x^2}{2x^2+3x-4}
What is
x\rightarrow-\infty, f(x) \rightarrow -7/2
and
x\rightarrow\infty, f(x) \rightarrow -7/2?
500
This is x for the following exponential problem:
2(3^{2x+5})+7=15
What is
x=\frac{log_3(4)-5}{2}?
500
This is the graph of the following rational function:
g(x)=\frac{(x-4)^2(x+2)}{(x+1)(x-3)(x-5)}
What is
