Podcast
Questions and Answers
Which of the following best describes the graph (it's a circle on a graph that hits all fours)?
Which of the following best describes the graph (it's a circle on a graph that hits all fours)?
- It is not a function (correct)
- It is a linear function
- It is a function
- It is a quadratic function
What statement best describes the function f(x)=2x^3+2x^2-x?
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.
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)?
Which of the following functions is graphed below (it's an open dot at (2,10) and closed dot at (2,5)?
Using the graph below, select all the statements that are true (has lines at every number with a filled and open dot).
Using the graph below, select all the statements that are true (has lines at every number with a filled and open dot).
What is f(1) and f(-1) for the function f(x)={-x+1, x<0}?
What is f(1) and f(-1) for the function f(x)={-x+1, x<0}?
Which equation matches the graph of the greatest integer function given below?
Which equation matches the graph of the greatest integer function given below?
Which of the following function is graphed below?
Which of the following function is graphed below?
WHICH OF THE FOLLOWING FUNCTIONS IS GRAPHED BELOW (-6,-4)?
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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