QuestionDetermine the range of the function $f(x)=3x+2$ for the domain $\{0,2,4,6\}$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=3x+$ . The domain of the function is $\{0,,4,6\}$

STEP 2

To find the range of a function, we need to substitute each value from the domain into the function and calculate the corresponding output.

STEP 3

Substitute $x=0$ into the function.
$f(0)=3(0)+2$

STEP 4

Calculate the function value at $x=0$ .
$f(0)=3(0)+2=2$

STEP 5

Substitute $x=2$ into the function.
$f(2)=3(2)+2$

STEP 6

Calculate the function value at $x=2$ .
$f(2)=3(2)+2=8$

STEP 7

Substitute $x=4$ into the function.
$f(4)=3(4)+2$

STEP 8

Calculate the function value at $x=4$ .
$f(4)=3(4)+2=14$

STEP 9

Substitute $x=6$ into the function.
$f(6)=3(6)+2$

STEP 10

Calculate the function value at $x=6$ .
$f(6)=3(6)+2=20$

STEP 11

The range of a function is the set of all possible output values. So, the range of the function $f(x)=3x+$ for the domain $\{0,,4,6\}$ is the set of all function values we calculated.
$Range = \{f(0), f(), f(4), f(6)\}$

STEP 12

Substitute the calculated function values into the range.
$Range = \{2,8,14,20\}$ The range of the function $f(x)=x+2$ for the domain $\{0,2,4,6\}$ is $\{2,8,14,20\}$ .

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