Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = |x| + 1

검증된 단계별 안내

Step 1: Understand the equation y = |x| + 1. This is an absolute value function, where |x| represents the absolute value of x. The graph of |x| is a V-shaped graph, and the '+1' shifts the graph vertically upward by 1 unit.

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, calculate y by substituting x into the equation y = |x| + 1. Remember that the absolute value of a number is always non-negative.

Step 3: For example, when x = -3, |x| = 3, so y = 3 + 1 = 4. Similarly, calculate y for all other x-values: -2, -1, 0, 1, 2, and 3.

Step 4: Plot the points (x, y) on a coordinate plane using the calculated values from the table. For instance, plot points like (-3, 4), (-2, 3), (-1, 2), (0, 1), (1, 2), (2, 3), and (3, 4).

Step 5: Connect the points to form the graph. The graph will have a V-shape, with the vertex at (0, 1) and the arms of the V extending symmetrically upward. This is the graph of y = |x| + 1.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Absolute Value Function

The absolute value function, denoted as |x|, measures the distance of a number x from zero on the number line, always yielding a non-negative result. For example, |3| = 3 and |-3| = 3. This function is crucial for understanding how the graph behaves, as it creates a V-shape, reflecting the positive and negative values of x symmetrically.

Graphing Linear Equations

Graphing linear equations involves plotting points on a coordinate plane that satisfy the equation. In this case, the equation y = |x| + 1 can be graphed by calculating y for various x values. The resulting points are then connected to form the graph, which illustrates the relationship between x and y visually.

Transformations of Functions

Transformations of functions involve shifting, reflecting, or stretching the graph of a function. In the equation y = |x| + 1, the '+1' indicates a vertical shift of the absolute value graph upwards by one unit. Understanding transformations helps in predicting how changes to the equation affect the graph's position and shape.

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3 y = |x| + 1