Name that mathematical object
For a function f, this is the set of real numbers which may be "plugged in" to f and is usually written in interval notation.
What is the domain of f?
A function f(x) has this on its graph when
limx->oo f(x) = 5
What is a horizontal asymptote at y=5?
Known across the world for its ability to help you take the derivative of a fraction, this derivative rule has a nice little mnemonic device to help you remember it.
What is the Quotient Rule (bonus 50 pts, what is the mnemonic device!)
This famous equation would help us solve a related rates question in which a ladder is sliding down a wall.
What is the Pythagorean Theorem?
What are the two real roots of the quadratic polynomial x2-5x+6 ?
This special type of function has a constant average rate of change on every choice of interval on its domain.
What is a linear function?
A function f(x) has this on its graph when
limx->3 f(x) = -oo.
What is a vertical asymptote at x=3
This function is the derivative of
x2(3x-7x4)
What is 9x2-42x5?
This is true about a function f on an interval (a,b), if f' is negative on (a, b).
What is: f is decreasing on (a, b)?
What is [6,inf]?
These x-values are important when doing curve sketching, and can be found by finding both roots of the derivative and places where the derivative does not exist.
What are Critical points/values?
A function f(x) has this on its graph if:
f(-4) is undefined, but
limx-> -4 f(x) = ½
What is a hole at (4,1/2)?
This function is the derivative of
(6x+9)1/3
This seven word sentence sums up what we know about the continuity of algebraic functions.
What is: Algebraic functions are continuous on their domain?
This is the piecewise function representation of the following function: f(x)=|2x-3|
What is:
2x-3 for x>2/3, -2x+3 for x<=3/2
This quantity is used to help determine if a quadratic function has real roots.
What is the discriminant?
or
What is b2-4ac?
These types of limit forms are not acceptable answers, but let you know that you must use algebra or another math tool to further investigate the limit. eg:
0/0, inf/inf, inf-inf, 0(inf)
What are indeterminate limit forms?
This function is the derivative of
(x1/3-1/x)-2
-2(x1/3-1/x)-3(1/3x-2/3-x-2)
This function is dy/dx for the following equation:
y2+x3-x2y2=7
what is dy/dx=(-3x2+2xy2)/(2y-2x2y)
What is the discriminant of the quadratic function
f(x)=6x2-12x+9?
D=144-4(6)(9)=144-216=-72
This particular type of line intersects a function at exactly one point (nearby), and has the same slope as the function at the point of intersection.
What is a tangent line?
A function f(x) has this on its graph if:
f(3)=0,
limx->3- f(x) = 0, and
limx->3+ f(x) = 3.
What is a jump discontinuity at x=3? (left continuous)
This function is the derivative of
[x2+x-1+7]/[(x+1)1/2]
What is [(2x-x-2)(x+1)1/2-1/2(x2+x-1+7)]/[x+1]
This quantity tells us whether a function will increase or decrease faster or slower.
What is the second derivative?
This power function is the most simplified version of
f(x)= [(2x)3+8x17/5]/[x2/5+1]?
What is 8x3