## Questions and Answers

Which of the following best describes the graph (it's a circle on a graph that hits all fours)?

What statement best describes the function f(x)=2x^3+2x^2-x?

It is a one-to-many function.

The greatest integer function shown below is defined so that it produces the greatest integer ______ or equal to x.

less than

Which of the following functions is graphed below (it's an open dot at (2,10) and closed dot at (2,5)?

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Using the graph below, select all the statements that are true (has lines at every number with a filled and open dot).

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What is f(1) and f(-1) for the function f(x)={-x+1, x<0}?

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Which equation matches the graph of the greatest integer function given below?

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Which of the following function is graphed below?

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WHICH OF THE FOLLOWING FUNCTIONS IS GRAPHED BELOW (-6,-4)?

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## Study Notes

### Graph Characteristics and Functions

- A circle on a graph that intersects all four quadrants is not classified as a function due to the vertical line test.
- The function ( f(x) = 2x^3 + 2x^2 - x ) is identified as one-to-many, indicating multiple outputs for a single input.

### Greatest Integer Function

- The greatest integer function delivers the greatest integer less than or equal to ( x ).
- The graph representation includes both open and closed dots, indicating the values that are included or excluded from the function.

### Specific Function Evaluations

- For the function defined as ( f(x) = {-x+1, x < 0} ), specific evaluations yield ( f(1) = 0 ) and ( f(-1) = 2 ).
- The representation ( Y = [X] - 2 ) corresponds to the graph of the greatest integer function.

### Function Graph Interpretation

- A function graphed with an open dot at (2,10) and a closed dot at (2,5) suggests the function ( Y = {x^3 - 3, x \leq 2} ), where the inequality features a line beneath it.
- Another function ( Y = {X^2 + 4, x \geq 2} ) also features a line under the inequality symbol.

### Evaluating Graphs

- The graph exhibiting lines at every integer with filled and open dots exemplifies the greatest integer function.
- A function represented as ( Y = |X + 3| - 4 ) can be identified by analyzing the coordinates, particularly (-6, -4).

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## Description

Test your knowledge on graphing functions with this quiz focused on understanding various functions and their characteristics. Each flashcard presents a question about graph properties, continuity, and types of functions. Perfect for students wanting to solidify their grasp of graphing concepts.