MATH 1324 Section 2.1 Quiz

What is the graph of the equation $x = y^2 + 5$ based on the following points?

What is the graph of the equation $y = -2x^3$ based on the following points?

Does the following table specify a function? Domain Range: (4, 3), (8, 6), (12, 5)

Does the following table specify a function? Domain Range: (-11, 20), (-18, 17), (-17, -13), (7, -5)

Does the given graph specify a function?

Does the equation $2xy = 9$ represent y as a function of x?

What type of function is specified by the equation $y = 6x + rac{1}{2}(3 - 12x)$?

Determine $y$ to the nearest integer for $y = f(3)$ based on the graph of function $f$.

What are the values of $x$ such that $f(x) = 0$?

What is the domain of the function $F(x) = 4x^3 + 2x^2$?

Graphs and Functions

For the function ( x = y^2 + 5 ), points used for graphing include (5, 0), (6, 1), (6, -1), (7, 1.41), and (7, -1.41). Use point-by-point plotting for visualization.
The function ( y = -2x^3 ) is graphed using points (-2, 16), (-1, 2), (0, 0), (1, -2), and (2, -16), illustrating the shape and behavior of cubic functions.

Function Specifications

The provided table indicates that a function is defined for inputs (domain) of 4, 8, and 12, yielding outputs (range) of 3, 6, and 5 respectively, validating it as a function.
In contrast, another table shows inputs (-11, -18, -17, 7) that produce varied outputs (20, 17, -13, -5); since -17 maps to two different outputs, this does not qualify as a function.

Graphical Function Identification

Certain graphs can indicate whether a function exists, with one graph confirming it does specify a function while another shows it does not, adhering to the vertical line test for functions.

Functional Representation

The equation ( 2xy = 9 ) displays y as a function of x, affirmatively establishing a relationship between the two variables.
A specific linear function is identified through the equation ( y = 6x + \frac{1}{2}(3 - 12x) ), indicating it is linear, constant, or neither.

Evaluating Function Values

For the function graph ( f ), evaluate ( y = f(3) ) where ( y ) approximates to -7 based on graphical representation.
The value of ( x ) where ( f(x) = 0 ) is found at x = -5, 0, and 8, determining the points where the function intersects the x-axis.

Domain of Functions

The domain of the cubic function ( F(x) = 4x^3 + 2x^2 ) is identified as ( (-\infty, \infty) ), implying it encompasses all real numbers.

Test your knowledge of graphing equations and functions in MATH 1324 Section 2.1. This quiz involves point-by-point plotting for various equations, including quadratic and cubic functions. Determine whether given tables represent functions and enhance your understanding of graphical representation in mathematics.