Chapter 3, Problem 2CR

Which of the following points are on the graph of, $y=x^3-3x+1$?

a. $\left(-2,-1\right)$

b. $\left(2,3\right)$

c. $\left(3,1\right)$

To determine

To calculate: Which of the given points are on the graph of $y=x^3-3x+1$.

Answer to Problem 2CR

Solution:

The points on the graph are

a. $(-2,-1)$

b. $(2,3)$

Explanation of Solution

Given:

The given points are

a. $(-2,-1)$

b. $(2,3)$

c. $(3,1)$

Formula used:

In order to find if the point $(x,y)$ are on the graph of a function $y=f(x)$ then substitute the values of $y$ and $x$ in the given equation and check if it satisfies.

Calculation:

a. $(x,y)=(-2,-1)$

We have the function $y=x^3-3x+1$

Substituting for $x$ and $y$ in the above equation, we get

$\begin{array}{l}-1=(-2{)}^3-3(-2)+1\\ \Rightarrow -1=-8+6+1=-1\end{array}$

Thus, we have seen that the point satisfies the given equation.

Thus, the point $(-2,-1)$ is on the graph of $y=x^3-3x+1$

b. $(x,y)=(2,3)$

We have the function $y=x^3-3x+1$

Substituting for $x$ and $y$ in the above equation, we get

$\begin{array}{l}3=(2{)}^3-3(2)+1\\ \Rightarrow 3=8-6+1=3\end{array}$

Thus, we have seen that the point satisfies the given equation.

Thus, the point $(3,1)$ is on the graph of $y=x^3-3x+1$

c. $(x,y)=(3,1)$

We have the function $y=x^3-3x+1$

Substituting for $x$ and $y$ in the above equation, we get

$1=(3{)}^3-3(3)+1$

$\Rightarrow 1=27-9+1$

The equation is not satisfied.

Therefore, the point $(3,1)$ is not on the graph of $y=x^3-3x+1$