Concept explainers
Use a table of values to graph each equation. State the domain and range.
Answer to Problem 1QC
The domain is all real numbers. The range is all real numbers.
Explanation of Solution
Given:
The equation:
Concept Used:
A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is sometimes called a straight line or, more archaically, a right line, to emphasize that it has no "wiggles" anywhere along its length.
The domain of a function is the complete set of possible values of the independent variable. The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
The range of a function is the complete set of all possible resulting values of the dependent variable ( y, usually), after we have substituted the domain.
Calculation:
The equation:
Make table to get some points on the graph
x | (x, y) | |
0 | (0, 3) | |
−2 | (− 2 , 1 ) | |
−5 | (− 5 ,− 2 ) | |
1 | (1, 4) | |
3 | ( 3 , 6 ) |
Graph the ordered pairs, and connect them to create a smooth curve. The straight line is having x and y intercept at x = − 3 and y = 3. Extended both sides to infinity
Slope − intercept form of a straight line is y = mx + b
Where m is the slope of the line and b is the y − intercept. The graph is a straight line with a slope − 1 The graph is a straight line. The domain is all real numbers. The range is all real numbers. |
Thus, the domain is all real numbers. The range is all real numbers.
Chapter 9 Solutions
Algebra 1
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