Greatest Integer Function Quiz & Flashcards

Questions and Answers

Which of the following best describes the graph? (It's a circle on a graph, it hits all four)

It is a linear function

It is not a function (correct)

It is a function

It is a quadratic function

Which statement best describes the function below: f(x) = 2x^3 + 2x^2 - x

It is one-to-one

It is one-to-many (correct)

It is a constant function

It is a linear 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 a closed dot at (2,5)

Y = {x^3 - 3, x < 2} Signup and view all the answers

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

f(-3.4) = -4 Signup and view all the answers

Given the function f(x) = {-x + 1, x < 0; 0, x ≥ 0}, what is f(1)?

0 Signup and view all the answers

Given the function f(x) = {-x + 1, x < 0; 0, x ≥ 0}, what is f(-1)?

1 Signup and view all the answers

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

Y = [X] - 2 Signup and view all the answers

Which of the following functions is graphed below?

Y = X^2 + 4, X ≤ 2 Signup and view all the answers

Which of the following functions is graphed below? (Points (-6,-4))

Y = |X + 3| - 4 Signup and view all the answers

Study Notes

Graphing Functions Overview

A circle graph that intersects all four quadrants does not represent a function due to the vertical line test.
A cubic function like f(x)=2x^3+2x^2-x is classified as a one-to-many function based on its outputs for unique inputs.

Greatest Integer Function Characteristics

The greatest integer function outputs the largest integer less than or equal to a given x value, often referred to as the "floor" function.
The graph of the greatest integer function features open and closed dots to denote values and continuity.

Function Graph Interpretations

A graph with an open dot at (2,10) and a closed dot at (2,5) corresponds to a piecewise function: Y={x^3-3 for x < 2; x^2 for x ≥ 2.
The greatest integer function graph includes filled dots indicating inclusive values at specified integers.

Evaluating Piecewise Functions

For the piecewise function f(x)={-x+1 for x < 0; x for x ≥ 0, specific evaluations include f(1)=0 and f(-1)=2, demonstrating the function's behavior at different x values.

Identifying Greatest Integer Function Graphs

The equation for a vertical transformation of the greatest integer function can be represented as Y=[X]-2, which shifts the graph down by two units.

Additional Graph Representations

The function Y={X^2+4; x^2 with a greater than or equal to sign represents a parabolic shape above the line y=4, indicating a minimum point.
The absolute value function represented by Y=|X+3|-4 has a vertex at (-3, -4) and opens upwards, typical of absolute value graphs.

Description

Test your knowledge of graphing functions with this quiz based on Apex 2.2.3. Understand concepts like whether a graph represents a function and the behavior of different types of functions. Challenge yourself with specific questions about mathematical definitions and properties.