QuestionEvaluate the function $f(x)=\frac{2}{5} x-\frac{5}{2}$ . What is $f(5)$ ? Options: A) $\frac{1}{2}$ B) $5$ C) $-\frac{1}{2}$ . What is $f(10)$ ? Options: A) $\frac{3}{2}$ B) $10$ C) $f(x)$ D) $f\left(\frac{3}{2}\right)$ .

Studdy Solution

STEP 1

Assumptions1. The function is defined as $f(x)=\frac{}{5} x-\frac{5}{}$ . We are asked to evaluate the function at $x=5$ and $x=10$

STEP 2

First, let's evaluate the function at $x=5$ . We can do this by substituting $x=5$ into the function.
$f(5)=\frac{2}{5} \cdot5-\frac{5}{2}$

STEP 3

Now, simplify the expression.
$f(5)=2-\frac{5}{2}$

STEP 4

To subtract the fractions, we need to have the same denominator. Convert the integer2 into a fraction with denominator2.
$2=\frac{4}{2}$ $f()=\frac{4}{2}-\frac{}{2}$

STEP 5

Subtract the fractions.
$f(5)=\frac{4}{2}-\frac{5}{2}=-\frac{1}{2}$ So, the correct function notation when $x=5$ is $f(5)=-\frac{1}{2}$ .

STEP 6

Next, let's evaluate the function at $x=10$ . We can do this by substituting $x=10$ into the function.
$f(10)=\frac{2}{5} \cdot10-\frac{5}{2}$

STEP 7

Now, simplify the expression.
$f(10)=4-\frac{5}{2}$

STEP 8

Again, to subtract the fractions, we need to have the same denominator. Convert the integer4 into a fraction with denominator2.
$4=\frac{8}{2}$ $f(10)=\frac{8}{2}-\frac{5}{2}$

STEP 9

Subtract the fractions.
$f()=\frac{8}{2}-\frac{5}{2}=\frac{3}{2}$ So, the correct description for the function notation $f()$ is "The output is $\frac{3}{2}$ when the input is".

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QuestionEvaluate the function $f(x)=\frac{2}{5} x-\frac{5}{2}$ . What is $f(5)$ ? Options: A) $\frac{1}{2}$ B) $5$ C) $-\frac{1}{2}$ . What is $f(10)$ ? Options: A) $\frac{3}{2}$ B) $10$ C) $f(x)$ D) $f\left(\frac{3}{2}\right)$ .

Studdy Solution

STEP 1

Assumptions1. The function is defined as $f(x)=\frac{}{5} x-\frac{5}{}$ . We are asked to evaluate the function at $x=5$ and $x=10$

STEP 2

First, let's evaluate the function at $x=5$ . We can do this by substituting $x=5$ into the function.
$f(5)=\frac{2}{5} \cdot5-\frac{5}{2}$

STEP 3

Now, simplify the expression.
$f(5)=2-\frac{5}{2}$

STEP 4

To subtract the fractions, we need to have the same denominator. Convert the integer2 into a fraction with denominator2.
$2=\frac{4}{2}$ $f()=\frac{4}{2}-\frac{}{2}$

STEP 5

Subtract the fractions.
$f(5)=\frac{4}{2}-\frac{5}{2}=-\frac{1}{2}$ So, the correct function notation when $x=5$ is $f(5)=-\frac{1}{2}$ .

STEP 6

Next, let's evaluate the function at $x=10$ . We can do this by substituting $x=10$ into the function.
$f(10)=\frac{2}{5} \cdot10-\frac{5}{2}$

STEP 7

Now, simplify the expression.
$f(10)=4-\frac{5}{2}$

STEP 8

Again, to subtract the fractions, we need to have the same denominator. Convert the integer4 into a fraction with denominator2.
$4=\frac{8}{2}$ $f(10)=\frac{8}{2}-\frac{5}{2}$

STEP 9

Subtract the fractions.
$f()=\frac{8}{2}-\frac{5}{2}=\frac{3}{2}$ So, the correct description for the function notation $f()$ is "The output is $\frac{3}{2}$ when the input is".

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Studdy Solution

STEP 1

Assumptions1. The function is defined as f(x)=5x−5f(x)=\frac{}{5} x-\frac{5}{}f(x)=5​x−5​ . We are asked to evaluate the function at x=5x=5x=5 and x=10x=10x=10

STEP 2

First, let's evaluate the function at x=5x=5x=5. We can do this by substituting x=5x=5x=5 into the function.f(5)=25⋅5−52f(5)=\frac{2}{5} \cdot5-\frac{5}{2}f(5)=52​⋅5−25​

STEP 3

Now, simplify the expression.f(5)=2−52f(5)=2-\frac{5}{2}f(5)=2−25​

STEP 4

To subtract the fractions, we need to have the same denominator. Convert the integer2 into a fraction with denominator2.2=422=\frac{4}{2}2=24​f()=42−2f()=\frac{4}{2}-\frac{}{2}f()=24​−2​

STEP 5

Subtract the fractions.f(5)=42−52=−12f(5)=\frac{4}{2}-\frac{5}{2}=-\frac{1}{2}f(5)=24​−25​=−21​So, the correct function notation when x=5x=5x=5 is f(5)=−12f(5)=-\frac{1}{2}f(5)=−21​.

STEP 6

Next, let's evaluate the function at x=10x=10x=10. We can do this by substituting x=10x=10x=10 into the function.f(10)=25⋅10−52f(10)=\frac{2}{5} \cdot10-\frac{5}{2}f(10)=52​⋅10−25​

STEP 7

Now, simplify the expression.f(10)=4−52f(10)=4-\frac{5}{2}f(10)=4−25​

STEP 8

Again, to subtract the fractions, we need to have the same denominator. Convert the integer4 into a fraction with denominator2.4=824=\frac{8}{2}4=28​f(10)=82−52f(10)=\frac{8}{2}-\frac{5}{2}f(10)=28​−25​

STEP 9

Subtract the fractions.f()=82−52=32f()=\frac{8}{2}-\frac{5}{2}=\frac{3}{2}f()=28​−25​=23​So, the correct description for the function notation f()f()f() is "The output is 32\frac{3}{2}23​ when the input is".

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Assumptions1. The function is defined as $f(x)=\frac{}{5} x-\frac{5}{}$ . We are asked to evaluate the function at $x=5$ and $x=10$

First, let's evaluate the function at $x=5$ . We can do this by substituting $x=5$ into the function.
$f(5)=\frac{2}{5} \cdot5-\frac{5}{2}$

Now, simplify the expression.
$f(5)=2-\frac{5}{2}$

To subtract the fractions, we need to have the same denominator. Convert the integer2 into a fraction with denominator2.
$2=\frac{4}{2}$ $f()=\frac{4}{2}-\frac{}{2}$

Subtract the fractions.
$f(5)=\frac{4}{2}-\frac{5}{2}=-\frac{1}{2}$ So, the correct function notation when $x=5$ is $f(5)=-\frac{1}{2}$ .

Next, let's evaluate the function at $x=10$ . We can do this by substituting $x=10$ into the function.
$f(10)=\frac{2}{5} \cdot10-\frac{5}{2}$

Now, simplify the expression.
$f(10)=4-\frac{5}{2}$

Again, to subtract the fractions, we need to have the same denominator. Convert the integer4 into a fraction with denominator2.
$4=\frac{8}{2}$ $f(10)=\frac{8}{2}-\frac{5}{2}$

Subtract the fractions.
$f()=\frac{8}{2}-\frac{5}{2}=\frac{3}{2}$ So, the correct description for the function notation $f()$ is "The output is $\frac{3}{2}$ when the input is".