Questions: Consider the following function. t(x)=4 ⌊ x/3 ⌋ Step 1 of 2: Identify the general shape of the graph of this function.

Consider the following function. t(x)=4 ⌊ x/3 ⌋ Step 1 of 2: Identify the general shape of the graph of this function.
Transcript text: Consider the following function. \[ t(x)=4 \llbracket \frac{x}{3} \rrbracket \] Step 1 of $\mathbf{2 :}$ : Identify the general shape of the graph of this function.
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Solution

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Solution Steps

Step 1: Analyze the given function

The given function is _f(x) = 4[x/3]_. The square brackets represent the greatest integer function (also known as the floor function). This function returns the largest integer less than or equal to its input. For example, [2.7] = 2, [3] = 3, and [-1.2] = -2. This means the function's output jumps at every integer multiple of 3.

Step 2: Determine the graph's general shape

The greatest integer function creates a step-like graph. The multiplier (4) stretches the graph vertically. The division by 3 within the brackets stretches it horizontally. Therefore, the graph will consist of horizontal line segments (steps) where each step has a length of 3 and rises by 4.

Final Answer: The first graph (top-left) correctly represents the function.

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