Math / Algebra

Questionomplete the table. $f(x)=\left\{\begin{array}{ll} 36-x^{2}, & x<6 \\ x-6, & x \geq 6 \end{array}\right.$ \begin{tabular}{|l|l|l|l|l|l|} \hline $x$ & 4 & 5 & 6 & 7 & 8 \\ \hline $f(x)$ & & & & & \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The function $f(x)$ is defined piecewise with different expressions for $x < 6$ and $x \geq 6$ .
2. We need to evaluate $f(x)$ at specific values $x = 4, 5, 6, 7, 8$ and fill in the corresponding $f(x)$ values in the table.

STEP 2

1. Evaluate $f(x)$ for $x = 4$ .
2. Evaluate $f(x)$ for $x = 5$ .
3. Evaluate $f(x)$ for $x = 6$ .
4. Evaluate $f(x)$ for $x = 7$ .
5. Evaluate $f(x)$ for $x = 8$ .

STEP 3

Evaluate $f(x)$ for $x = 4$ .
Since $x = 4 < 6$ , use the expression $f(x) = 36 - x^2$ .
$f(4) = 36 - 4^2 = 36 - 16 = 20$

STEP 4

Evaluate $f(x)$ for $x = 5$ .
Since $x = 5 < 6$ , use the expression $f(x) = 36 - x^2$ .
$f(5) = 36 - 5^2 = 36 - 25 = 11$

STEP 5

Evaluate $f(x)$ for $x = 6$ .
Since $x = 6 \geq 6$ , use the expression $f(x) = x - 6$ .
$f(6) = 6 - 6 = 0$

STEP 6

Evaluate $f(x)$ for $x = 7$ .
Since $x = 7 \geq 6$ , use the expression $f(x) = x - 6$ .
$f(7) = 7 - 6 = 1$

STEP 7

Evaluate $f(x)$ for $x = 8$ .
Since $x = 8 \geq 6$ , use the expression $f(x) = x - 6$ .
$f(8) = 8 - 6 = 2$
The completed table is:
\begin{tabular}{|l|l|l|l|l|l|} \hline x & 4 & 5 & 6 & 7 & 8 \\ \hline f(x) & 20 & 11 & 0 & 1 & 2 \\ \hline \end{tabular}

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Questionomplete the table. $f(x)=\left\{\begin{array}{ll} 36-x^{2}, & x<6 \\ x-6, & x \geq 6 \end{array}\right.$ \begin{tabular}{|l|l|l|l|l|l|} \hline $x$ & 4 & 5 & 6 & 7 & 8 \\ \hline $f(x)$ & & & & & \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The function $f(x)$ is defined piecewise with different expressions for $x < 6$ and $x \geq 6$ .
2. We need to evaluate $f(x)$ at specific values $x = 4, 5, 6, 7, 8$ and fill in the corresponding $f(x)$ values in the table.

STEP 2

1. Evaluate $f(x)$ for $x = 4$ .
2. Evaluate $f(x)$ for $x = 5$ .
3. Evaluate $f(x)$ for $x = 6$ .
4. Evaluate $f(x)$ for $x = 7$ .
5. Evaluate $f(x)$ for $x = 8$ .

STEP 3

Evaluate $f(x)$ for $x = 4$ .
Since $x = 4 < 6$ , use the expression $f(x) = 36 - x^2$ .
$f(4) = 36 - 4^2 = 36 - 16 = 20$

STEP 4

Evaluate $f(x)$ for $x = 5$ .
Since $x = 5 < 6$ , use the expression $f(x) = 36 - x^2$ .
$f(5) = 36 - 5^2 = 36 - 25 = 11$

STEP 5

Evaluate $f(x)$ for $x = 6$ .
Since $x = 6 \geq 6$ , use the expression $f(x) = x - 6$ .
$f(6) = 6 - 6 = 0$

STEP 6

Evaluate $f(x)$ for $x = 7$ .
Since $x = 7 \geq 6$ , use the expression $f(x) = x - 6$ .
$f(7) = 7 - 6 = 1$

STEP 7

Evaluate $f(x)$ for $x = 8$ .
Since $x = 8 \geq 6$ , use the expression $f(x) = x - 6$ .
$f(8) = 8 - 6 = 2$
The completed table is:
\begin{tabular}{|l|l|l|l|l|l|} \hline x & 4 & 5 & 6 & 7 & 8 \\ \hline f(x) & 20 & 11 & 0 & 1 & 2 \\ \hline \end{tabular}

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Questionomplete the table. f(x)={36−x2,x<6x−6,x≥6f(x)=\left\{\begin{array}{ll} 36-x^{2}, & x<6 \\ x-6, & x \geq 6 \end{array}\right.f(x)={36−x2,x−6,​x<6x≥6​ \begin{tabular}{|l|l|l|l|l|l|} \hlinexxx & 4 & 5 & 6 & 7 & 8 \\ \hlinef(x)f(x)f(x) & & & & & \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The function f(x) f(x) f(x) is defined piecewise with different expressions for x<6 x < 6 x<6 and x≥6 x \geq 6 x≥6.2. We need to evaluate f(x) f(x) f(x) at specific values x=4,5,6,7,8 x = 4, 5, 6, 7, 8 x=4,5,6,7,8 and fill in the corresponding f(x) f(x) f(x) values in the table.

STEP 2

1. Evaluate f(x) f(x) f(x) for x=4 x = 4 x=4.2. Evaluate f(x) f(x) f(x) for x=5 x = 5 x=5.3. Evaluate f(x) f(x) f(x) for x=6 x = 6 x=6.4. Evaluate f(x) f(x) f(x) for x=7 x = 7 x=7.5. Evaluate f(x) f(x) f(x) for x=8 x = 8 x=8.

STEP 3

Evaluate f(x) f(x) f(x) for x=4 x = 4 x=4.Since x=4<6 x = 4 < 6 x=4<6, use the expression f(x)=36−x2 f(x) = 36 - x^2 f(x)=36−x2.f(4)=36−42=36−16=20 f(4) = 36 - 4^2 = 36 - 16 = 20 f(4)=36−42=36−16=20

STEP 4

Evaluate f(x) f(x) f(x) for x=5 x = 5 x=5.Since x=5<6 x = 5 < 6 x=5<6, use the expression f(x)=36−x2 f(x) = 36 - x^2 f(x)=36−x2.f(5)=36−52=36−25=11 f(5) = 36 - 5^2 = 36 - 25 = 11 f(5)=36−52=36−25=11

STEP 5

Evaluate f(x) f(x) f(x) for x=6 x = 6 x=6.Since x=6≥6 x = 6 \geq 6 x=6≥6, use the expression f(x)=x−6 f(x) = x - 6 f(x)=x−6.f(6)=6−6=0 f(6) = 6 - 6 = 0 f(6)=6−6=0

STEP 6

Evaluate f(x) f(x) f(x) for x=7 x = 7 x=7.Since x=7≥6 x = 7 \geq 6 x=7≥6, use the expression f(x)=x−6 f(x) = x - 6 f(x)=x−6.f(7)=7−6=1 f(7) = 7 - 6 = 1 f(7)=7−6=1

STEP 7

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Questionomplete the table. $f(x)=\left\{\begin{array}{ll} 36-x^{2}, & x<6 \\ x-6, & x \geq 6 \end{array}\right.$ \begin{tabular}{|l|l|l|l|l|l|} \hline $x$ & 4 & 5 & 6 & 7 & 8 \\ \hline $f(x)$ & & & & & \\ \hline \end{tabular}

1. The function $f(x)$ is defined piecewise with different expressions for $x < 6$ and $x \geq 6$ .
2. We need to evaluate $f(x)$ at specific values $x = 4, 5, 6, 7, 8$ and fill in the corresponding $f(x)$ values in the table.

1. Evaluate $f(x)$ for $x = 4$ .
2. Evaluate $f(x)$ for $x = 5$ .
3. Evaluate $f(x)$ for $x = 6$ .
4. Evaluate $f(x)$ for $x = 7$ .
5. Evaluate $f(x)$ for $x = 8$ .

Evaluate $f(x)$ for $x = 4$ .
Since $x = 4 < 6$ , use the expression $f(x) = 36 - x^2$ .
$f(4) = 36 - 4^2 = 36 - 16 = 20$

Evaluate $f(x)$ for $x = 5$ .
Since $x = 5 < 6$ , use the expression $f(x) = 36 - x^2$ .
$f(5) = 36 - 5^2 = 36 - 25 = 11$

Evaluate $f(x)$ for $x = 6$ .
Since $x = 6 \geq 6$ , use the expression $f(x) = x - 6$ .
$f(6) = 6 - 6 = 0$

Evaluate $f(x)$ for $x = 7$ .
Since $x = 7 \geq 6$ , use the expression $f(x) = x - 6$ .
$f(7) = 7 - 6 = 1$