Questions: If f(x)=int(3 x), find: (a) f(1.3) (b) f(3.2) (c) f(-1.7) (a) f(1.3)= (Simplify your answer.)

If f(x)=int(3 x), find: (a) f(1.3) (b) f(3.2) (c) f(-1.7) (a) f(1.3)= (Simplify your answer.)
Transcript text: If $f(x)=\operatorname{int}(3 x)$, find: (a) $f(1.3)$ (b) $f(3.2)$ (c) $f(-1.7)$ (a) $f(1.3)=$ $\square$ (Simplify your answer.)
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Solution

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Solution Steps

Step 1: Multiply the input \(x\) by the coefficient \(k\)

To find the value of \(f(x) = \operatorname{int}(kx)\) for \(k = 3\) and \(x = 1.3\), we first calculate the product \(kx\). \[kx = 3 \times 1.3 = 3.9\]

Step 2: Apply the integer part function

Next, we apply the integer part function \(\operatorname{int}(\cdot)\) to \(kx\), which involves taking the integer part of \(kx\), effectively discarding any fractional part. For \(kx = 3.9\), the integer part is \(\operatorname{int}(3.9) = 3\).

Final Answer:

The value of \(f(x) = \operatorname{int}(kx)\) for \(k = 3\) and \(x = 1.3\) is \(f(x) = 3\).

Step 1: Multiply the input \(x\) by the coefficient \(k\)

To find the value of \(f(x) = \operatorname{int}(kx)\) for \(k = 3\) and \(x = 3.2\), we first calculate the product \(kx\). \[kx = 3 \times 3.2 = 9.6\]

Step 2: Apply the integer part function

Next, we apply the integer part function \(\operatorname{int}(\cdot)\) to \(kx\), which involves taking the integer part of \(kx\), effectively discarding any fractional part. For \(kx = 9.6\), the integer part is \(\operatorname{int}(9.6) = 9\).

Final Answer:

The value of \(f(x) = \operatorname{int}(kx)\) for \(k = 3\) and \(x = 3.2\) is \(f(x) = 9\).

Step 1: Multiply the input \(x\) by the coefficient \(k\)

To find the value of \(f(x) = \operatorname{int}(kx)\) for \(k = 3\) and \(x = -1.7\), we first calculate the product \(kx\). \[kx = 3 \times -1.7 = -5.1\]

Step 2: Apply the integer part function

Next, we apply the integer part function \(\operatorname{int}(\cdot)\) to \(kx\), which involves taking the integer part of \(kx\), effectively discarding any fractional part. For \(kx = -5.1\), the integer part is \(\operatorname{int}(-5.1) = -5\).

Final Answer:

The value of \(f(x) = \operatorname{int}(kx)\) for \(k = 3\) and \(x = -1.7\) is \(f(x) = -5\).

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