Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problem 43a

Chapter 2, Problem 43a

Use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each.

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Observe the graph and identify the points where the curve crosses the x-axis. These points are the x-intercepts. The x-intercepts occur when the y-value is 0.

From the graph, locate the x-coordinates of the points where the curve intersects the x-axis. These are the x-intercepts.

Next, identify the point where the curve crosses the y-axis. This point is the y-intercept. The y-intercept occurs when the x-value is 0.

From the graph, locate the y-coordinate of the point where the curve intersects the y-axis. This is the y-intercept.

Summarize the x-intercepts and y-intercept based on the observations from the graph.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

X-Intercepts

X-intercepts are the points where a graph crosses the x-axis. At these points, the value of y is zero. To find the x-intercepts, one can set the function equal to zero and solve for x. In graphical terms, these are the horizontal intersections of the curve with the x-axis.

Y-Intercepts

Y-intercepts are the points where a graph crosses the y-axis, occurring when the value of x is zero. To determine the y-intercept, substitute x = 0 into the function and solve for y. Graphically, these points represent the vertical intersections of the curve with the y-axis.

Graph Interpretation

Graph interpretation involves analyzing the visual representation of a function to extract meaningful information, such as intercepts, trends, and behavior at extremes. Understanding how to read a graph, including the significance of axes and tick marks, is crucial for accurately identifying intercepts and other features of the function.

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In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 1 - x/2 > 4

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Solve and check: 24 + 3 (x + 2) = 5(x − 12).

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In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 3 - √-7)²

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Textbook Question

Use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each.

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Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 7/2x - 5/3x = 22/3

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Solve each equation in Exercises 41–60 by making an appropriate substitution. $9 x^{4} = 25 x^{2} - 16$

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