Algebra I Unit 2 - Functions

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Across
  1. 4. The X _________ is the point where the line crosses the x-axis. We can say that the X ______is the value of the x coordinate of a point where the value of y coordinate is equal to zero.
  2. 6. An________ variable is a variable that represents a quantity that is being manipulated in an experiment. x is often the variable used to represent the _________ variable in an equation.
  3. 8. An _______notation is a way to describe continuous sets of real numbers by the numbers that bound them. In other words a way of writing subsets of the real number line
  4. 9. A _________ or “round brackets” are the familiar symbols used in pairs to group things together or specify the order of operations in an equation. They help in grouping numbers and defining the order of operations.
  5. 12. We can also define the increasing and _______ intervals using the first derivative of the function f(x) as: If f'(x) ≥ 0 on I, then I is said to be an increasing interval. If f'(x) ≤ 0 on I, then it is said to be a ______ interval.
  6. 13. The vertical line test is used to find if a line is a ______. If the line does not pass the vertical line test then it is not a ____.
  7. 14. A__________ variable is a variable whose value depends upon independent variables. The dependent variable is what is being measured in an experiment or evaluated in a mathematical equation. The _______ variable is sometimes called "the outcome variable."
  8. 16. When graphing equations, where they intersect there are solutions. If the graphs do not intersect, ____________ line, there are no solutions. If the equations are the same, there are infinitely many solutions.
  9. 17. A ________ Line Test is a technique used to find if a line is a function or not. This test involves placing a vertical line through another line on a graph and seeing if the vertical line touches the original line more than once.
  10. 19. To find when a function is _______, you must first take the derivative, then set it equal to 0, and then find between which zero values the function is negative. Now test values on all sides of these to find when the function is negative, and therefore decreasing.
Down
  1. 1. In algebra, _________ are used to signify groupings of numbers that must be evaluated together, and any numbers appearing within ________ must be evaluated first. For example, in the expression 3 + (9 - 5), first, subtract 5 from 9, then add the result to 3.
  2. 2. The set of values that the function assumes. This is also one of the characteristics of a function
  3. 3. If the function's first derivative is f' (x) ≥ 0, the interval _________. On the other hand, if the value of the derivative f' (x) ≤ 0, then the interval is said to be a decreasing interval.
  4. 5. A function ____________ takes an input and produces an output. The formula for this world is y=f(x)
  5. 7. For a real-valued function f(x), the interval I is said to be an Interval of ________ if for every x < y, we have f(x) ≤ f(y). We can also define the intervals using the first derivative of the function f(x) as: If f'(x) ≥ 0 on I, then it is said to be an Interval of _____________.
  6. 10. An _______ compares two values, showing if one is less than, greater than, or simply not equal to another value. Example: a ≠ b says that a is not equal to b
  7. 11. The Y ______ of a graph is the point where the graph intersects the y-axis. We know that the x-coordinate of any point on the y-axis is 0. So the x-coordinate of a Y ________ is 0.
  8. 14. The set of values that are allowed to plug into a function. This is also one of the characteristics of a function.
  9. 15. On a multiple-choice math problem, if there are variables in the answer choices, this tells you that you can ______ in values (meaning choose your own numbers) for those variables, in order to simplify the question.
  10. 18. A collection of ordered pairs containing one object from each set. If the object x is from the first set and the object y is from the second set, then the objects are said to be related if the ordered pair (x,y) is in the _______. A function is a type of ________.