Question

writing function rules write a function rule for the statement.

1. the output is half of the input.
2. the output is eleven more than the input.
3. the output is three less than the input.
4. the output is the cube of the input.
5. the output is six times the input.
6. the output is one more than twice the input.

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chapter 7 functions

Explanation:

Step1: Define input variable

Let the input be $x$, output be $f(x)$.

Step2: Translate #9 to function

Half the input means $\frac{1}{2}x$.
$f(x)=\frac{1}{2}x$

Step3: Translate #10 to function

11 more than input: $x+11$.
$f(x)=x+11$

Step4: Translate #11 to function

3 less than input: $x-3$.
$f(x)=x-3$

Step5: Translate #12 to function

Cube of input: $x^3$.
$f(x)=x^3$

Step6: Translate #13 to function

6 times input: $6x$.
$f(x)=6x$

Step7: Translate #14 to function

Twice input plus 1: $2x+1$.
$f(x)=2x+1$

Answer:

1. $f(x)=\frac{1}{2}x$
2. $f(x)=x+11$
3. $f(x)=x-3$
4. $f(x)=x^3$
5. $f(x)=6x$
6. $f(x)=2x+1$