Properties of Real Numbers, Equations, Inequalities
This property of real numbers states that c(a+b) = ca + cb.
What is the distributive property?
This is the value of f(3) if f(x) = 3x + 1.
What is 10?
If the graph of a function is moving up as it goes from left to right on a certain interval, we could say it is doing this.
What is increasing?
|x| can be better understood if we note this represents the distance between x and this number.
What is 0?
This is the resulting quadratic when you multiply out (3x - 2)(2x + 1) and write in standard form, combining all like terms.
What is 6x2 - x - 2?
This is the value of x that solves the equation 3(x-2)+11=5.
What is x = 0?
This is the value of x when f(x) = 11, given f(x) = 5 - 2x.
What is -3?
If a function is moving horizontally, not up nor down, as it traces from left to right on an interval, we may say it is doing this.
What is staying constant?
Two matrices A and B must have this if we are to add them together.
What are identical dimensions?
This is the resulting complex number in a + bi form when you multiply out (3 - 3i)(2 + 5i). Recall that i2 = -1.
What is 21 + 9i?
This is the interval containing all x-values that satisfy the inequality 3x + 10 < 15.
If g(x) = 4x - 7, and f(x) has a graph perpendicular to g(x) and intersecting it at its y-intercept, this is the equation of f(x).
What is f(x) = (1/4)x - 7?
We call the point where a function intersects the x-axis this.
What is a zero, a solution, a root, or where f(x) = 0?
These are the buttons I hit on the TI-84 to pull up my matrix menu.
What is Alpha -> Zoom?
(3 - 2i) and (3 + 2i) are examples of this vocabulary term.
What are complex conjugates?
This type of equation, when attempting to solve it, results in a statement that is obviously false, like 0 = 3.
What is an equation with no solution?
If g(x) = (1/2)x + 4, and f(x) is parallel to g(x) and passes through the point (-2, 8), this is the equation for f(x).
What is f(x) = (1/2)x + 9?
This describes what a function f(x) is doing as x goes off towards positive infinity.
What is right end behavior?
This is the ordered pair solving the system of equations below.
x - 2y = 10
-2x + 8y = -12
What is (14, 2)?
These are the solutions to the factorable quadratic equation x2 - 5x + 4 = 0.
What are x = 1 and x = 4?
This interval describes all x-values that satisfy the compound inequality 4 < 2x - 2 < 6.
What is (3,4)?
What is f(x) = (-3/4)x + (1/4)?
Regardless of the function involved, f-1(f(x)) should always equal this.
What is x?
What is an inconsistent system?
These are the solutions to the unfactorable quadratic equation 4.8x2 - 17.1x + 10 = 24 rounded to three decimal places.
What are x = -0.686 and x = 4.249?