Question

How do you graph $y = {x^5}$ by plotting points?

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 a 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 $y = {x^5}$. Let we substitute the value of x as $0$, $1$, and $-1$.
Step 1: Now we consider the value of x as $0$, the value of y is
$ \Rightarrow y = {0^5}$
$ \Rightarrow y = 0$
Step 2: Now, we consider the value of x as $1$, the value of y is
$ \Rightarrow y = {1^5}$
$ \Rightarrow y = 1$
Step 3: Now we consider the value of x as $-1$, the value of y is
$ \Rightarrow y = {(-1)^5}$
$ \Rightarrow y = -1$
Step 4: Now we consider the value of x as $2$, the value of y is
$ \Rightarrow y = {2^5}$
$ \Rightarrow y = 32$
Step 5: Now we consider the value of x as $-2$, the value of y is
$ \Rightarrow y = {(-2)^5}$
$ \Rightarrow y = -32$
Now we draw a table for these values we have

x	$0$	$1$	$ - 1$
y	$0$	$1$	$ - 1$

The graph plotted for these point is represented below:

Note:
The graph plotted is of two dimensional. The graph is plotted in x-axis versus y axis. 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 because the value of y depends on the value of x.