Illustrative Math Alignment: Grade 7 Unit 5

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

Topic

Rational Functions

Description

This example demonstrates the graph of the rational function y = 1 / x. The graph is a hyperbola with vertical and horizontal asymptotes, with the vertical asymptote occurring at x = 0. Students are tasked with graphing the function and determining its vertical asymptote.

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = (x - 5) / (x + 4). The graph features a vertical asymptote at x = -4 and displays two branches, one in the first quadrant and one in the third quadrant. Students are asked to graph the function and identify its vertical asymptote.

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = (x - 1) / (x - 3). The graph features a vertical asymptote at x = 3 and displays two distinct branches, one in the first quadrant and another in the third quadrant. Students are tasked with graphing the function and identifying its vertical asymptote.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = (x + 1) / ((x + 2)(x + 4)). The graph features two vertical asymptotes at x = -2 and x = -4, and displays three distinct branches, with one in each of the first, second, and third quadrants. Students are asked to graph the function and identify its vertical asymptotes.

Topic

Rational Functions

Description

This example presents the graph of the rational function y = (x - 3) / ((x + 3)(x + 5)). The graph features vertical asymptotes at x = -3 and x = -5, illustrating how the function behaves near these lines. Students are tasked with graphing the function and determining its vertical asymptotes.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = (x + 3) / ((x - 1)(x + 4)). The graph features vertical asymptotes at x = -4 and x = 1, displaying how the function behaves near these lines. Students are asked to graph the function and identify its vertical asymptotes.

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = (x + 4) / ((x + 2)(x - 5)). The graph features vertical asymptotes at x = -2 and x = 5, demonstrating the behavior of the function near these asymptotes. Students are tasked with graphing the function and determining its vertical asymptotes.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = (x - 9) / ((x - 1)(x + 3)). The graph features vertical asymptotes at x = -3 and x = 1, showing the function's behavior around these asymptotes. Students are asked to graph the function and identify its vertical asymptotes.

Topic

Rational Functions

Description

This example presents the graph of the rational function y = (x - 1) / ((x - 2)(x - 3)). The graph features vertical asymptotes at x = 2 and x = 3, marked with dashed red lines. Students are tasked with graphing the function and determining its vertical asymptotes.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = (x - 8) / ((x + 3)(x - 3)). The graph features vertical asymptotes at x = -3 and x = 3, highlighted by dashed red lines. Students are asked to graph the function and identify its vertical asymptotes.

Topic

Rational Functions

Description

This example presents the graph of the rational function y = -(x + 1) / (x + 2). The graph features a single vertical asymptote at x = -2, indicated by a dashed red line. Students are tasked with graphing the function and determining its vertical asymptote.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = -1 / x. The graph is a hyperbola with vertical and horizontal asymptotes, with the vertical asymptote at x = 0. Students are asked to graph the function and identify its vertical asymptote.

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = -(x - 3) / (x + 4). The graph features a vertical asymptote at x = -4, but it is incorrectly labeled as x = -2. Students are asked to graph the function and identify its vertical asymptote.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = -(x - 5) / (x - 4). The graph features a vertical asymptote at x = 4, which is correctly labeled. Students are tasked with graphing the function and determining its vertical asymptote.

Topic

Rational Functions

Description

This example presents the graph of the rational function y = -(x + 2) / ((x + 4)(x + 1)). The graph features vertical asymptotes at x = -4 and x = -1. Students are asked to graph the function and identify its vertical asymptotes.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = -(x - 4) / ((x + 5)(x + 2)). The graph features vertical asymptotes at x = -5 and x = -2. Students are tasked with graphing the function and determining its vertical asymptotes.

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = -(x + 2) / ((x - 3)(x + 7)). The graph features vertical asymptotes at x = -7 and x = 3. Students are asked to graph the function and identify its vertical asymptotes.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = -(x + 1) / ((x + 2)(x - 8)). The graph features vertical asymptotes at x = -2 and x = 8. Students are tasked with graphing the function and determining its vertical asymptotes.

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = -(x - 4) / ((x - 3)(x + 2)). The graph features vertical asymptotes at x = -2 and x = 3. Students are asked to graph the function and identify its vertical asymptotes.

Topic

Rational Functions

Description

This example presents the graph of the rational function y = -(x - 3) / ((x + 3)(x - 1)). The graph features vertical asymptotes at x = -3 and x = 1. Students are tasked with graphing the function and determining its vertical asymptotes.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = -(x - 1) / ((x - 2)(x - 3)). The graph features vertical asymptotes at x = 2 and x = 3, marked with dashed red lines on the coordinate plane. Students are asked to graph the function and identify its vertical asymptotes.

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = 1 / (x + 2). The graph is a hyperbola with a vertical asymptote at x = -2. Students are tasked with graphing the function and determining its vertical asymptote.

Topic

Rational Functions

Description

This example presents the graph of the rational function y = 1 / (x - 4). The graph is a hyperbola with a vertical asymptote at x = 4. Students are asked to graph the function and identify its vertical asymptote.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = 1 / (5x + 3). The graph features a vertical asymptote at x = -0.6, indicated by a dashed red line. Students are tasked with graphing the function and determining its vertical asymptote.

Topic

Rational Functions

Description

This example demonstrates the graph of the rational function y = -1 / (6x + 2). The graph features a vertical asymptote at x = -1/3, shown with a dashed red line on the grid. Students are asked to graph the function and identify its vertical asymptote.

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = 1 / (5x - 7). The graph features a vertical asymptote at x = 1.4, marked by a dashed red line on the grid. Students are tasked with graphing the function and determining its vertical asymptote.

Topic

Rational Functions

Description

This example presents the graph of the rational function y = 1 / (-9x + 3). The graph is plotted on a grid with a vertical asymptote at x = 1/3, marked by a dashed red line. Students are asked to graph the function and identify its vertical asymptote.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = (x + 3) / (x + 2). The graph features a vertical asymptote at x = -2 and shows two branches, one in the second quadrant and one in the fourth quadrant. Students are tasked with graphing the function and determining its vertical asymptote.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

Topic

Rational Functions

Description

This math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / x. The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph is a hyperbola with branches in the first and third quadrants, illustrating the characteristic shape of this basic rational function.

Topic

Rational Functions

Description

This math example focuses on creating a table of x-y coordinates and graphing the function y = -1 / (x - 1). The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph includes labeled points at certain coordinates, illustrating how the negative sign in the numerator and the constant in the denominator affect the graph's shape and position.

Topic

Rational Functions

Description

This math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (-x - 1). The image showcases both the table of x-y coordinates and the resulting graph. The graph is plotted with labeled points at given coordinates, illustrating how the negative sign and constant in the denominator affect the graph's shape and position.

Topic

Rational Functions

Description

This math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (-x - 1). The image presents both the table of x-y coordinates and the resulting graph. The graph includes points labeled at specified coordinates, demonstrating how the negative signs in both the numerator and denominator, along with the constant, affect the graph's shape and position.

Topic

Rational Functions

Description

This math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / (x + 1) + 1. The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The table contains specific x-y coordinates: (-2, 0), (-1.5, -1), (0, 2), (1.5, 1.4), (2, 1.333), which are plotted on the graph. This example illustrates how adding a constant to a rational function affects its graph.

Topic

Rational Functions

Description

This math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (x + 1) - 1. The image showcases both the table of x-y coordinates and the resulting graph. The table contains specific x-y coordinates: (-2, -2), (-1.5, -3), (0, 0), (1.5, -0.6), (2, -0.667), which are plotted on the graph. This example illustrates how subtracting a constant from a rational function affects its graph.