Complete the input-output table for the function f(x)=(x−2)2+3

Question

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3
.(2 points)
x f(x)
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1 f(1)=
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1
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2 f(2)=
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3 f(3)=
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3
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4 f(4)=
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4
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Answer 1

To complete the input-output table for the function $f(x)=(x-2{)}^2+3$, we will calculate $f(x)$ for each given value of $x$.

1. For $x=1$: $$f(1)=(1-2{)}^2+3=(-1{)}^2+3=1+3=4$$

2. For $x=2$: $$f(2)=(2-2{)}^2+3=(0{)}^2+3=0+3=3$$

3. For $x=3$: $$f(3)=(3-2{)}^2+3=(1{)}^2+3=1+3=4$$

4. For $x=4$: $$f(4)=(4-2{)}^2+3=(2{)}^2+3=4+3=7$$

Now, we can fill out the input-output table:

$$\text{Misplaced hline}$$

So the final answers are:

• $f(1)=4$
• $f(2)=3$
• $f(3)=4$
• $f(4)=7$