Q31. - Algebra 2

Question

Graph each relation or equation and find the domain and range. 

Then determine whether the relation or equation is a function. 

$y=3x-4$

Step-by-Step Solution

Answer

The graph of the given equation is:

The domain and range of the given equation are all real numbers. The given equation is a function.

Step 1 – Vertical line test, domain and range.

• The graph represents a function if no vertical line intersects the graph on more than one point. The graph does not represent a function if some vertical line intersects the graph on two or more points.
• The set of input values is known as domain.
• The set of output values is known as Range.

Step 2 – Draw the graph of the given relation.

The given equation is $y=3x-4$.

The table of vales for the given equation is:

$\begin{array}{cc}x& y\\ -2& -10\\ -1& -7\\ 0& -4\\ 1& -1\\ 2& 2\end{array}$

Plot these ordered pairs on a coordinate plane and connect them by a straight line as shown below:

Step 3 – Domain and range of the given equation.

The given equation represents a straight line. The given equation is defined for all real values of $x$. So, the domain of the given equation is all real numbers.

Every real number is the $y$-coordinate of some point on the line. So, the range of the given equation is all real numbers.

Step 4 – Check whether the equation is a function.

The above graph passes the vertical line test. For each $x$ value, there is exactly one $y$ value. So, the given equation is a function.

 Thus, the domain of the given equation is all real numbers and the range of the given equation is all real numbers. The given equation is a function.