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Math  /  Algebra

QuestionFill in the table using this function rule. f(x)=x+9f(x)=\sqrt{x+9}
Simplify your answers as much as possible. Click "Not a real number" if applicable. \begin{tabular}{|c|c|} \hlinexx & f(x)f(x) \\ \hline-23 & □\square \\ \hline-13 & □\square \\ \hline-9 & □\square \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? We're plugging numbers into the function f(x)=x+9 f(x) = \sqrt{x+9} and finding out what comes out!
If we can't find a real number, we'll say so. Watch out! Remember, square roots of negative numbers aren't real!
If the stuff inside the square root is negative, we need to click "Not a real number."

STEP 2

1. Evaluate for x=−23 x = -23
2. Evaluate for x=−13 x = -13
3. Evaluate for x=−9 x = -9

STEP 3

**Plug in** x=−23 x = -23 into the function:
f(−23)=−23+9 f(-23) = \sqrt{-23 + 9}

STEP 4

**Calculate** the inside of the square root:
−23+9=−14 -23 + 9 = -14

STEP 5

**Check** if the result inside the square root is non-negative.
Since −14-14 is negative, we have a problem!
**Conclusion:** For x=−23 x = -23 , the result is "Not a real number."

STEP 6

**Plug in** x=−13 x = -13 into the function:
f(−13)=−13+9 f(-13) = \sqrt{-13 + 9}

STEP 7

**Calculate** the inside of the square root:
−13+9=−4 -13 + 9 = -4

STEP 8

**Check** if the result inside the square root is non-negative.
Since −4-4 is negative, we can't find a real number here either.
**Conclusion:** For x=−13 x = -13 , the result is "Not a real number."

STEP 9

**Plug in** x=−9 x = -9 into the function:
f(−9)=−9+9 f(-9) = \sqrt{-9 + 9}

STEP 10

**Calculate** the inside of the square root:
−9+9=0 -9 + 9 = 0

STEP 11

**Check** if the result inside the square root is non-negative.
Since 00 is non-negative, we can find the square root.

STEP 12

**Simplify** the square root:
0=0 \sqrt{0} = 0
**Conclusion:** For x=−9 x = -9 , the result is 00.

STEP 13

xf(x)−23Not a real number−13Not a real number−90\begin{array}{|c|c|} \hline x & f(x) \\ \hline -23 & \text{Not a real number} \\ \hline -13 & \text{Not a real number} \\ \hline -9 & 0 \\ \hline \end{array}

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