## 7 Must-See Mathematics Movies Inspired by True Events

I have watched many movies about mathematics, mathematicians, and about mathematics teachers, but I particularly like the seven below because they were inspired by true events. Although many of them diverge from actual events, I still find them more realistic compared to other movies of the same genre. For those who have not watched these movies, don’t worry as there are no spoilers in the descriptions.

1.) Stand and Deliver (1988)

Main Cast: Edward James Olmos

Stand and Deliver tells a story of high school teacher Jaime Escalante who inspired his troublesome and dropout prone students in Garfield High School to learn calculus. Many of his students pass the AP Calculus exam only to be accused by the testing board of cheating.

2.) A Beautiful Mind (2001)

Main Cast: Russell Crowe

A Beautiful Mind is a biographical film based on the life of mathematician John Forbes Nash. It centers in his struggle against paranoid schizophrenia and his relationship with his wife.  Continue reading…

## Understanding Domain and Range Part 4

In this post, we summarize the previous three articles about domain and range. In the first part of the series, we focused on the graphical meaning of domain and range. We have learned that the domain of a function can be interpreted as the projection of its graph to the x-axis. Similarly, the range of the function is the projection of its graph to the y-axis.

Graphical meaning of domain (red) and range (green)

In the second part of the series, we learned to analyze equations of functions to determine their domain and range. We learned the restrictions in the domain and range of functions are affected by the following: squares in the expressions, square root signs, absolute value signs, and being in the denominator. In exploring these we concluded the following:

• Expressions under the square root sign result to a positive real number or 0.  This means that we have to set the inequality such that the expression is greater than or equal to 0, and then find the permissible values of x.
• Expressions containing squares result to a positive real number or 0. This affects the range of the function.
• Expressions inside the absolute value sign result to a positive number of 0. This also affects the range of the function.
• Expressions in the denominator of fractions cannot be 0 because it will make the function undefined. So, we need to find the value of x that makes the denominator by 0. To do this, we equate the expression in the denominator to 0 and find the value of x. The values of x are the restrictions in the domain.

In the third part of the series, we examined functions that have more complicated equations than those in the second part of the series.

Before I end this series, there is one more concept about domain that I want you to remember. That is, the domain of all polynomial functions is the set of real numbers. That’s why the domain of linear functions and quadratic functions in Part 1 and Part 2 is the set of real numbers.

## Understanding Domain and Range Part 3

In the previous post, we have learned how to analyze equations of functions and determine their domain and range. We have observed that the range of the functions $y = x^2$ and $y = |x|$ are the set of real numbers greater than or equal to $0$ since squaring a number or getting its absolute value results to $0$ or a positive real number. We also learned the value under the square root sign must be greater than or equal to 0. Lastly, we have learned that we cannot divide by zero because it will make the function undefined.

In this post, we are going to continue our discussion by examining functions with equations more complicated than those in the second part of this series.

Squares and Absolute Values

1. $f(x) = x^2 - 3$

Domain: The function is defined for any real number $x$, so the domain of $f$ is the set of real numbers.

Range: The minimum value of $x^2$ is $0$ for any real number $x$ and $f(0) - 3 = 0^2 - 3 = -3$. So, the minimum value of the function is $-3$. We can make the value of the function as large as possible by increasing the absolute value of $x$. So, the range of the function is the set of real numbers greater than or equal to $-3$ or $[-3, \infty)$ in interval notation.  Continue reading…