Q9. - Algebra 2

Question

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

Then determine whether the relation or equation is a function.

 

$y=-2x+1$

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=-2x+1.

The table of vales for the given equation is:

$\begin{array}{cc}x& y\\ -2& 5\\ -1& 3\\ 0& 1\\ 1& -1\\ 2& -3\end{array}$

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.