Q60. - Algebra 1

Question

Compare and contrast the graphs of $y=2x+1$ with the domain $\{1,2,3,4\}$ and $y=2x+1$ with the domain of all real numbers.

Step-by-Step Solution

Answer

The comparison between graphs of $y=2x+1$ with the domain $\{1,2,3,4\}$ and $y=2x+1$ with the domain of all real numbers is that the graph of $y=2x+1$ with the domain $\{1,2,3,4\}$ is a graph having only four points and the graph of $y=2x+1$ with the domain of all real numbers is a straight line.

Part a. Step 1. Draw the graph of y = 2 x + 1 with the domain { 1 , 2 , 3 , 4 } and y = 2 x + 1 with the domain of all real numbers .

The domain is the set of values of the independent variable for which the function is defined.

From the given function $y=2x+1$, it can be noticed that $x$ is the independent variable.

Therefore, the domain of the function $y=2x+1$ is the set of values of $x$ for which the function is defined.

The graph of the function $y=2x+1$ with the domain $\{1,2,3,4\}$ can be plotted by plotting the points having $x$ values as 1,2,3 and 4.

Therefore, the graph of the function $y=2x+1$ with the domain $\{1,2,3,4\}$ is:

The graph of the function $y=2x+1$ with the domain of all real numbers can be plotted by plotting the points having $x$ values as the set of real numbers.

Therefore, the graph of the function $y=2x+1$ with the domain of all real numbers is:

Part a. Step 2. Compare and contrast the graphs of y = 2 x + 1 with the domain { 1 , 2 , 3 , 4 } and y = 2 x + 1 with the domain of all real numbers.

From the graphs of $y=2x+1$ with the domain $\{1,2,3,4\}$ and $y=2x+1$ with the domain of all real numbers it can be noticed that the graph of $y=2x+1$ with the domain  $\{1,2,3,4\}$ is a graph having only four points and the graph of $y=2x+1$ with the domain of all real numbers is a straight line.

Therefore, the comparison between graphs of $y=2x+1$ with the domain $\{1,2,3,4\}$ and $y=2x+1$ with the domain of all real numbers is that the graph of $y=2x+1$ with the domain $\{1,2,3,4\}$ is a graph having only four points and the graph of $y=2x+1$ with the domain of all real numbers is a straight line.