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 the leading term of the polynomial:
p(x)=x^4+3x^3-3x^2-7x+6
What is
x^4?
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 following transformation of the function on the board
2f(x+3)+1
What is?
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
This is the solution to the following linear system:
(2x+3y=5),(3x-y=-9)
What is
(-2,3)?
300
This is the composition f(g(x)) of
f(x) = (4x+5) / (x-4)
g(x) = 3/x^2
What is
f^(-1)(x)=(12+5x^2)/(3-4x^2)
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 y-intercept for the following function:
g(x)=\frac{x^2-4}{x^2-2x-10}
What is
(0,\frac{2}{5})?
300
This is the value in 2045 for a deposit of $23,000 made in 2005 in a continuously compounding account with 4% interest.
What is
23000e^(1.6)?
300
This is the solution to the augmented matrix for the following equations:
{(3x+2y-z=10),(x-2y+z=2),(-x+y-3z=0):}
What is
(3,0,-1)?
400
The inverses for the functions below:
f(x)=-root(3)(x+1)+2
g(x) = (4x+5)/(x-4)
What is
f^-1(x)=(2-x)^3-1?
g^-1(x)=(4x+5)/(x-4)
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 the equation and graph for a logarithmic base 3 function with a vertical asymptote at x=-2, a reflection over the y-axis, and a vertical shift of -4
What is (see Desmos)?
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
