QuestionDetermine whether the relation $y = 6x + 12$ defines $y$ as a function of $x$ . Also, provide the domain of the function.

Studdy Solution

STEP 1

1. A relation defines $y$ as a function of $x$ if for every $x$ in the domain, there is exactly one corresponding $y$ .
2. The equation $y = 6x + 12$ is a linear equation.
3. The domain of a linear function is typically all real numbers unless otherwise restricted.

STEP 2

1. Determine if the relation defines $y$ as a function of $x$ .
2. Determine the domain of the function.

STEP 3

To determine if $y = 6x + 12$ defines $y$ as a function of $x$ , we need to check if for every $x$ there is exactly one $y$ .
Since the equation $y = 6x + 12$ is a linear equation, it represents a straight line. In a linear equation of the form $y = mx + b$ , for every value of $x$ , there is exactly one value of $y$ .
Therefore, the relation $y = 6x + 12$ does define $y$ as a function of $x$ .

STEP 4

Determine the domain of the function $y = 6x + 12$ .
For a linear function like $y = 6x + 12$ , there are no restrictions on the values that $x$ can take. Linear functions are defined for all real numbers.
Thus, the domain of the function is all real numbers, which can be expressed as:
$\text{Domain: } (-\infty, \infty)$
The relation $y = 6x + 12$ defines $y$ as a function of $x$ , and the domain of the function is all real numbers, $(-\infty, \infty)$ .

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