Questions and Answers
Which of the following best describes the graph (it's a circle on a graph it hits all fours)?
Which statement best describes the function below: $f(x) = 2x^3 + 2x^2 - x$?
It is a one-to-many
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 a 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(x) for $f(x) = {-x + 1, x<0}$?
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Which equation matches the graph of the greatest integer function given below?
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Which of the following functions is graphed below?
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Which of the following functions is graphed below (point (-6,-4))?
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Study Notes
Graph Function Characteristics
- A graph that forms a circle intersects all four quadrants; it does not represent a function due to the vertical line test.
- A cubic function f(x)=2x^3+2x^2-x is classified as one-to-many, meaning each input can produce multiple outputs.
Greatest Integer Function
- The greatest integer function defines its output as the largest integer less than or equal to x.
- This function is represented visually with steps, typically marked with closed (included) and open (excluded) dots.
Function Characteristics from Graphs
- A graph featuring an open dot at (2,10) and a closed dot at (2,5) indicates piecewise functions, specifically:
- Y={x^3-3 for x < 2
- Y=2 for x ≥ 2
Evaluating Piecewise Functions
- For the function f(x)={-x+1 for x < 0, x for x ≥ 0:
- Calculating specific values gives:
- f(1)=0 as x is greater or equal to 0
- f(-1)=2 as x is less than 0
- Calculating specific values gives:
Identifying Graph Types
- The equation that corresponds to the greatest integer function is Y=[X]-2, indicating a downward shift of the basic step function.
- Another piecewise function Y={X^2+4 for x < 2, Y=2 for x ≥ 2 includes parabolic growth and a horizontal line.
Absolute Value Functions
- A graph showing coordinates (-6,-4) corresponds to the equation Y=|X+3|-4, illustrating a transformation of the basic absolute value function.
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Description
This quiz covers the characteristics of various functions including cubic and piecewise functions. It explores how to evaluate and identify functions based on their graphs and the vertical line test. Test your understanding of different types of functions and their graphical representations.
