QuestionFind $f(7)$ , $f(-6)$ , $f(-3.8)$ , and $f(-5.4)$ for the piecewise function: $f(x) = \{-2x + 16 \text{ if } x \leq -4; 3 \text{ if } -4 < x < 3; x + 8 \text{ if } x \geq 3\}$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as a piecewise function with three different expressions. . We need to find the values of $f(7)$ , $f(-6)$ , $f(-3.8)$ , and $f(-5.4)$ .

STEP 2

To find the value of $f(7)$ , we need to identify which condition $x=7$ satisfies in the piecewise function.The conditions are1. $x \leq -4$
2. $-4 < x <$ . $x \geq$
Since $7 \geq$ , we use the third expression of the piecewise function, which is $x+8$ .

STEP 3

Substitute $x=7$ into the expression $x+8$ to find $f(7)$ .
$f(7) =7 +8$

STEP 4

Calculate the value of $f(7)$ .
$f(7) =7 +8 =15$

STEP 5

To find the value of $f(-)$ , we need to identify which condition $x=-$ satisfies in the piecewise function.Since $- \leq -4$ , we use the first expression of the piecewise function, which is $-2x+16$ .

STEP 6

Substitute $x=-6$ into the expression $-2x+16$ to find $f(-6)$ .
$f(-6) = -2(-6) +16$

STEP 7

Calculate the value of $f(-6)$ .
$f(-6) = -2(-6) +16 =12 +16 =28$

STEP 8

To find the value of $f(-3.8)$ , we need to identify which condition $x=-3.8$ satisfies in the piecewise function.Since $-4 < -3.8 <3$ , we use the second expression of the piecewise function, which is $3$ .

STEP 9

Since the function value is a constant $3$ for this range, we have $f(-3.8) =3$ .

STEP 10

To find the value of $f(-5.4)$ , we need to identify which condition $x=-5.4$ satisfies in the piecewise function.Since $-5.4 \leq -4$ , we use the first expression of the piecewise function, which is $-2x+16$ .

STEP 11

Substitute $x=-5.4$ into the expression $-x+16$ to find $f(-5.4)$ .
$f(-5.4) = -(-5.4) +16$

STEP 12

Calculate the value of $f(-5.4)$ .
$f(-5.4) = -2(-5.4) +16 =10.8 +16 =26.8$ So, the values are(a) $f(7) =15$ (b) $f(-6) =28$ (c) $f(-.8) =$ (d) $f(-5.4) =26.8$

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QuestionFind $f(7)$ , $f(-6)$ , $f(-3.8)$ , and $f(-5.4)$ for the piecewise function: $f(x) = \{-2x + 16 \text{ if } x \leq -4; 3 \text{ if } -4 < x < 3; x + 8 \text{ if } x \geq 3\}$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as a piecewise function with three different expressions. . We need to find the values of $f(7)$ , $f(-6)$ , $f(-3.8)$ , and $f(-5.4)$ .

STEP 2

To find the value of $f(7)$ , we need to identify which condition $x=7$ satisfies in the piecewise function.The conditions are1. $x \leq -4$
2. $-4 < x <$ . $x \geq$
Since $7 \geq$ , we use the third expression of the piecewise function, which is $x+8$ .

STEP 3

Substitute $x=7$ into the expression $x+8$ to find $f(7)$ .
$f(7) =7 +8$

STEP 4

Calculate the value of $f(7)$ .
$f(7) =7 +8 =15$

STEP 5

To find the value of $f(-)$ , we need to identify which condition $x=-$ satisfies in the piecewise function.Since $- \leq -4$ , we use the first expression of the piecewise function, which is $-2x+16$ .

STEP 6

Substitute $x=-6$ into the expression $-2x+16$ to find $f(-6)$ .
$f(-6) = -2(-6) +16$

STEP 7

Calculate the value of $f(-6)$ .
$f(-6) = -2(-6) +16 =12 +16 =28$

STEP 8

To find the value of $f(-3.8)$ , we need to identify which condition $x=-3.8$ satisfies in the piecewise function.Since $-4 < -3.8 <3$ , we use the second expression of the piecewise function, which is $3$ .

STEP 9

Since the function value is a constant $3$ for this range, we have $f(-3.8) =3$ .

STEP 10

To find the value of $f(-5.4)$ , we need to identify which condition $x=-5.4$ satisfies in the piecewise function.Since $-5.4 \leq -4$ , we use the first expression of the piecewise function, which is $-2x+16$ .

STEP 11

Substitute $x=-5.4$ into the expression $-x+16$ to find $f(-5.4)$ .
$f(-5.4) = -(-5.4) +16$

STEP 12

Calculate the value of $f(-5.4)$ .
$f(-5.4) = -2(-5.4) +16 =10.8 +16 =26.8$ So, the values are(a) $f(7) =15$ (b) $f(-6) =28$ (c) $f(-.8) =$ (d) $f(-5.4) =26.8$

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Studdy Solution

STEP 1

Assumptions1. The function f(x)f(x)f(x) is defined as a piecewise function with three different expressions. . We need to find the values of f(7)f(7)f(7), f(−6)f(-6)f(−6), f(−3.8)f(-3.8)f(−3.8), and f(−5.4)f(-5.4)f(−5.4).

STEP 2

STEP 3

Substitute x=7x=7x=7 into the expression x+8x+8x+8 to find f(7)f(7)f(7).f(7)=7+8f(7) =7 +8f(7)=7+8

STEP 4

Calculate the value of f(7)f(7)f(7).f(7)=7+8=15f(7) =7 +8 =15f(7)=7+8=15

STEP 5

To find the value of f(−)f(-)f(−), we need to identify which condition x=−x=-x=− satisfies in the piecewise function.Since −≤−4- \leq -4−≤−4, we use the first expression of the piecewise function, which is −2x+16-2x+16−2x+16.

STEP 6

Substitute x=−6x=-6x=−6 into the expression −2x+16-2x+16−2x+16 to find f(−6)f(-6)f(−6).f(−6)=−2(−6)+16f(-6) = -2(-6) +16f(−6)=−2(−6)+16

STEP 7

Calculate the value of f(−6)f(-6)f(−6).f(−6)=−2(−6)+16=12+16=28f(-6) = -2(-6) +16 =12 +16 =28f(−6)=−2(−6)+16=12+16=28

STEP 8

To find the value of f(−3.8)f(-3.8)f(−3.8), we need to identify which condition x=−3.8x=-3.8x=−3.8 satisfies in the piecewise function.Since −4<−3.8<3-4 < -3.8 <3−4<−3.8<3, we use the second expression of the piecewise function, which is 333.

STEP 9

Since the function value is a constant 333 for this range, we have f(−3.8)=3f(-3.8) =3f(−3.8)=3.

STEP 10

To find the value of f(−5.4)f(-5.4)f(−5.4), we need to identify which condition x=−5.4x=-5.4x=−5.4 satisfies in the piecewise function.Since −5.4≤−4-5.4 \leq -4−5.4≤−4, we use the first expression of the piecewise function, which is −2x+16-2x+16−2x+16.

STEP 11

Substitute x=−5.4x=-5.4x=−5.4 into the expression −x+16-x+16−x+16 to find f(−5.4)f(-5.4)f(−5.4).f(−5.4)=−(−5.4)+16f(-5.4) = -(-5.4) +16f(−5.4)=−(−5.4)+16

STEP 12

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Assumptions1. The function $f(x)$ is defined as a piecewise function with three different expressions. . We need to find the values of $f(7)$ , $f(-6)$ , $f(-3.8)$ , and $f(-5.4)$ .

Substitute $x=7$ into the expression $x+8$ to find $f(7)$ .
$f(7) =7 +8$

Calculate the value of $f(7)$ .
$f(7) =7 +8 =15$

To find the value of $f(-)$ , we need to identify which condition $x=-$ satisfies in the piecewise function.Since $- \leq -4$ , we use the first expression of the piecewise function, which is $-2x+16$ .

Substitute $x=-6$ into the expression $-2x+16$ to find $f(-6)$ .
$f(-6) = -2(-6) +16$

Calculate the value of $f(-6)$ .
$f(-6) = -2(-6) +16 =12 +16 =28$

To find the value of $f(-3.8)$ , we need to identify which condition $x=-3.8$ satisfies in the piecewise function.Since $-4 < -3.8 <3$ , we use the second expression of the piecewise function, which is $3$ .

Since the function value is a constant $3$ for this range, we have $f(-3.8) =3$ .

To find the value of $f(-5.4)$ , we need to identify which condition $x=-5.4$ satisfies in the piecewise function.Since $-5.4 \leq -4$ , we use the first expression of the piecewise function, which is $-2x+16$ .

Substitute $x=-5.4$ into the expression $-x+16$ to find $f(-5.4)$ .
$f(-5.4) = -(-5.4) +16$