Ch. 1 - Equations and Inequalities

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

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problem 44a

Chapter 2, Problem 44a

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.

Verified step by step guidance

Step 1: Observe the graph and identify the x-intercepts. The x-intercepts are the points where the curve crosses the x-axis. These points have a y-coordinate of 0.

Step 2: From the graph, locate the points where the curve intersects the x-axis. Based on the tick marks, the x-intercepts appear to be at x = -6, x = 0, and x = 6.

Step 3: Next, identify the y-intercept. The y-intercept is the point where the curve crosses the y-axis. This point has an x-coordinate of 0.

Step 4: From the graph, observe that the curve intersects the y-axis at the point (0, 0). This means the y-intercept is at y = 0.

Step 5: Summarize the findings: The x-intercepts are at x = -6, x = 0, and x = 6. The y-intercept is at y = 0.

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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 the context of the provided graph, identifying these points involves observing where the curve intersects 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. In the graph shown, the y-intercept can be found by locating the point where the curve meets 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 of the function. Understanding how to read a graph, including the significance of axes and tick marks, is crucial for accurately determining intercepts and other characteristics of the function depicted.

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Textbook Question

Solve each equation in Exercises 41–60 by making an appropriate substitution. x - 13√x + 40 = 0

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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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Textbook Question

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

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Textbook Question

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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Textbook Question

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $x^{2} - (1 / 3) x$

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Textbook Question

In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 8 + √-32)/24

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