Find the value of the function for the given value of x. ƒ(x)=[[x]], for x=(-π)
Table of contents
- 0. Review of Algebra4h 18m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations1h 43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 5m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 22m
- 10. Combinatorics & Probability1h 45m
2. Graphs of Equations
Two-Variable Equations
Problem 1
Textbook Question
Graph each equation in Exercises 1–4. Let x= -3, -2. -1, 0, 1, 2 and 3. y = 2x-2
Verified step by step guidance1
Step 1: Understand the equation y = 2x - 2. This is a linear equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Step 2: Create a table of values for x and y. Use the given x-values (-3, -2, -1, 0, 1, 2, 3). For each x-value, substitute it into the equation y = 2x - 2 to calculate the corresponding y-value.
Step 3: For example, when x = -3, substitute into the equation: y = 2(-3) - 2. Similarly, calculate y for all other x-values (-2, -1, 0, 1, 2, 3).
Step 4: Once you have the table of x and y values, plot these points on a coordinate plane. Each pair (x, y) represents a point on the graph.
Step 5: Draw a straight line through the plotted points, as the equation represents a linear function. Ensure the line extends in both directions and label the graph appropriately.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Linear Equations
A linear equation is an algebraic expression that represents a straight line when graphed on a coordinate plane. It typically takes the form y = mx + b, where m is the slope and b is the y-intercept. Understanding linear equations is essential for graphing, as it allows students to identify how changes in x affect y.
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Slope and Y-Intercept
The slope of a linear equation indicates the steepness and direction of the line, calculated as the change in y over the change in x (rise/run). The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero. In the equation y = 2x - 2, the slope is 2 and the y-intercept is -2, which are crucial for accurately plotting the graph.
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Graphing Points
Graphing points involves plotting specific (x, y) coordinates on a Cartesian plane. For the equation y = 2x - 2, students will substitute the given x-values (-3, -2, -1, 0, 1, 2, 3) to find corresponding y-values. This process helps visualize the relationship between x and y, forming the linear graph of the equation.
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