Question

How do you graph the line $ y = \left| { - x + 3} \right| - 4 $ ?

Answer 1

Hint: A graph of a function f is the set of ordered pairs; the equation of graph is generally represented as $ y = f\left( x \right) $ , where x and f(x) are real numbers. We substitute the value of x and we determine the value of y and then we mark the points in the graph and we join the points.

Complete step by step solution:
Here in this question, we have to plot the graph for the given function. A graph of a function is set of ordered pairs and it is represented as $ y = f\left( x \right) $ , where x and f(x) are real numbers. These pairs are in the form of cartesian form and the graph is the two-dimensional graph.
First, we have to find the value of y by using the graph equation $ y = \left| { - x + 3} \right| - 4 $ . Let we substitute the value of x as $ 0 $ , $ 1 $ , $ 2 $ , and $ 3 $ .
Now we consider the value of x as $ 0 $ , the value of y is
 $ \Rightarrow y = \left| { - 0 + 3} \right| - 4 $
 $ \Rightarrow y = \left| 3 \right| - 4 $
 $ \Rightarrow y = 3 - 4 $
 $ \Rightarrow y = - 1 $
Now we consider the value of x as $ 1 $ , the value of y is
 $ \Rightarrow y = \left| { - 1 + 3} \right| - 4 $
 $ \Rightarrow y = \left| 2 \right| - 4 $
 $ \Rightarrow y = 2 - 4 $
 $ \Rightarrow y = - 2 $
Now we consider the value of x as $ 2 $ , the value of y is
 $ \Rightarrow y = \left| { - 2 + 3} \right| - 4 $
 $ \Rightarrow y = \left| 1 \right| - 4 $
 $ \Rightarrow y = - 3 $
Now we consider the value of x as $ 3 $ , the value of y is
 $ \Rightarrow y = \left| { - 3 + 3} \right| - 4 $
 $ \Rightarrow y = - 4 $

Now we draw a table for these values we have

x	$ 0 $	$ 1 $	$ 2 $	$ 3 $
y	$ - 1 $	$ - 2 $	$ - 3 $	$ - 4 $

The graph plotted for these point is represented below:

Note: The graph is of two dimensional. By the equation of a graph, we can plot the graph by assuming the value of x. We can’t assume the value of y as the value of y depends on the value of x. When a modulus function is applied in front of a function, the function acquires positive value for any input value.