Graph each function. See Examples 1 and 2. ƒ(x)=3|x|

검증된 단계별 안내

Understand the function given: \(f(x) = 3|x|\). This means the output is three times the absolute value of \(x\).

Recall the shape of the basic absolute value function \(|x|\), which forms a 'V' shape with its vertex at the origin (0,0).

To graph \(f(x) = 3|x|\), multiply the output of \(|x|\) by 3, which vertically stretches the graph by a factor of 3. This makes the 'V' shape steeper.

Plot key points to guide your graph: for example, when \(x=0\), \(f(0) = 3|0| = 0\); when \(x=1\), \(f(1) = 3|1| = 3\); and when \(x=-1\), \(f(-1) = 3| -1| = 3\).

Draw the graph by connecting these points with straight lines forming a 'V' shape, ensuring the vertex is at the origin and the arms rise steeply due to the factor of 3.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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주요 개념

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

Absolute Value Function

The absolute value function, denoted |x|, outputs the non-negative value of x regardless of its sign. It creates a V-shaped graph symmetric about the y-axis, reflecting all negative inputs as positive outputs.

Vertical Stretching of Functions

Multiplying a function by a constant greater than 1, like 3 in 3|x|, stretches the graph vertically. This means all output values are scaled by that factor, making the graph steeper compared to the parent function.

Graphing Piecewise Functions

Absolute value functions can be viewed as piecewise functions with different expressions for x ≥ 0 and x < 0. Understanding this helps in plotting points accurately and visualizing the graph's shape.