MHF4U Grade 12 Advanced Functions Learning Log

Name: Assem Abizhanova Date: Thursday September 12^th^, 2024 Learning Logs MHF4U -- Grade 12 Advanced Functions For Shuntt Tanielian **Learning Goals:** - Practice Interval Notation - Recognize Polynomial Functions - Recognize Power functions - identify key characteristics of power fu...

Name: Assem Abizhanova Date: Thursday September 12^th^, 2024 Learning Logs MHF4U -- Grade 12 Advanced Functions For Shuntt Tanielian **Learning Goals:** - Practice Interval Notation - Recognize Polynomial Functions - Recognize Power functions - identify key characteristics of power functions - Describe End behaviours of Polynomial Functions **Tasks:** - As we get started make sure that your legal name is displayed on Zoom and that you are logged into Canvas. We will go over Lesson 2 today (as the second day of the term) but will also quicky go over Course Introduction and Interval Notation. (5 mins) - We are going to review interval notation and go over Polynomial and Power Functions. Some of the definitions and procedures will stick around for the whole course so make sure you ask any questions as they come up. (45 mins) - Practice time! (20 mins) - Complete you learning log questions below. - Complete the Discussion Board - Review the Course Introduction Material on Canvas - Complete the practice questions posted on Lesson 1 and 2 - Next Steps! - Complete Lesson 3 tomorrow - We will look at Lesson 5 and 6 on Monday. **Terminology:** **Polynomial Functions --** is a function like quadratic, linear, cubic, quartic and so on, involving only positive whole powers of x. Polynomials can have more than one term, that's why there is "poly" which means "many". **Power Functions -- power functions have a single term, but also they are allowed to have a negative or fractional exponent.** **End Behavior -- Long Run Behavior. It is basically a way of classifying what happens if x will go positive infinity, and what happens if x will get closer towards negative infinity.** **Even Function -- even functions are graphically symmetric about y-axis.** **Odd Function -- odd functions are symmetrical about origin.** **Solutions/Independent work** 1\) Answer the following questions about [*f*(*x*) = *x*^3^]{.math.inline} a\) Is it a polynomial? How do you know? It is polynomial, because the polynomial functions are defined as mathematical expressions that involve sum of powers in one or more variables. In this case, we have a monomial polynomial of degree 3/ cubic monomial. b\) What kind of function is it? (odd or even) Odd c\) What is its end behaviour?  d\) State it's Domain and Range. 2\) Answer the following questions about [*f*(*x*) = *x*^4^]{.math.inline} a\) Is it a polynomial? How do you know? It is polynomial, because the polynomial functions are defined as mathematical expressions that involve sum of powers in one or more variables. In this case, we have a monomial polynomial of degree 4/ quartic monomial. b\) What kind of function is it? (odd or even) Even c) What is its end behaviour? d\) State it's Domain and Range. **Self-reflection** What are your goals for this course? Achieve a perfect understanding in Advanced Functions. Also, get \~95% as my final grade for application to university.