Graph each function for the domain of real numbers. 1. y=x2+3 2. y=-2x2+5 3. y=2-2 %3D

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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## Exercises
Graph each function for the domain of real numbers.

1. \( y = x + 3 \)

The graph of \( y = x + 3 \) is a straight line with a slope of 1 and a y-intercept at (0, 3). When you plot the points and draw the line, it should pass through points like (1, 4) and (2, 5).

2. \( y = 2x + 5 \)

The graph of \( y = 2x + 5 \) is a straight line with a slope of 2 and a y-intercept at (0, 5). When you plot the points, the line will pass through points like (1, 7) and (2, 9).

3. \( y = 2x - 2 \)

The graph of \( y = 2x - 2 \) is a straight line with a slope of 2 and a y-intercept at (0, -2). When you plot the points, the line will pass through points like (1, 0) and (2, 2).

4. \( y = -\frac{1}{2}x + 3 \)

The graph of \( y = -\frac{1}{2}x + 3 \) is a straight line with a slope of -0.5 and a y-intercept at (0, 3). When you plot the points, the line will pass through points like (2, 2) and (4, 1).

### Graph Details:

Each graph has a coordinate plane with both x and y-axes marked from -3 to 3 on the y-axis and -6 to 6 on the x-axis.

For each graph:
- The x-axis is horizontal and denotes the independent variable.
- The y-axis is vertical and denotes the dependent variable.
- The scales on both axes are equally spaced, and each square represents 1 unit.

The direction of the line and its steepness is determined by the slope (coefficient of x):
- Positive slopes (\(+\)) incline upwards.
- Negative slopes (\(-\)) incline downwards.

The points are plotted based on substituting x values into the function equation to find corresponding y values.
Transcribed Image Text:## Exercises Graph each function for the domain of real numbers. 1. \( y = x + 3 \) The graph of \( y = x + 3 \) is a straight line with a slope of 1 and a y-intercept at (0, 3). When you plot the points and draw the line, it should pass through points like (1, 4) and (2, 5). 2. \( y = 2x + 5 \) The graph of \( y = 2x + 5 \) is a straight line with a slope of 2 and a y-intercept at (0, 5). When you plot the points, the line will pass through points like (1, 7) and (2, 9). 3. \( y = 2x - 2 \) The graph of \( y = 2x - 2 \) is a straight line with a slope of 2 and a y-intercept at (0, -2). When you plot the points, the line will pass through points like (1, 0) and (2, 2). 4. \( y = -\frac{1}{2}x + 3 \) The graph of \( y = -\frac{1}{2}x + 3 \) is a straight line with a slope of -0.5 and a y-intercept at (0, 3). When you plot the points, the line will pass through points like (2, 2) and (4, 1). ### Graph Details: Each graph has a coordinate plane with both x and y-axes marked from -3 to 3 on the y-axis and -6 to 6 on the x-axis. For each graph: - The x-axis is horizontal and denotes the independent variable. - The y-axis is vertical and denotes the dependent variable. - The scales on both axes are equally spaced, and each square represents 1 unit. The direction of the line and its steepness is determined by the slope (coefficient of x): - Positive slopes (\(+\)) incline upwards. - Negative slopes (\(-\)) incline downwards. The points are plotted based on substituting x values into the function equation to find corresponding y values.
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