MATH_REV_PART2_ECO220

MATH_REV_PART2_ECO220 - Math Review for ECO220Y PART 2 of 2...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math Review for ECO220Y: PART 2 of 2 For success in our course, it is important that you have the skills needed to solve the problems in both Part 1 and Part 2 of this Math Review. If you find these questions easy then you do not need to spend much time on this. However, if your skills are rusty or missing it is important that you work to get caught up. Both parts of this Math Review are here to help you. Additionally our Teaching Assistants (TA’s) have office hours should you run into difficulty when working through this Math Review. 1 Functions A function f is a rule that assigns to each element x in a set A exactly one element, called f ( x ), in a set B . It is common to write y = f ( x ). For example, if f ( x ) = 2 x + 1, one may write y = 2 x + 1. In this example we have a simple linear function: the equation of a line. In Problem Set #1 we looked at simple linear functions (including the constant function: a horizontal line). In this problem set we explore commonly used nonlinear functions, including how to find their slopes. 2 Power Functions One simple type of nonlinear function is a power function . A function of the form f ( x ) = x a , where a is a constant, is a power function. One power function you probably recall is the parabola. For example, y = x 2 is a power function (and in this example, it is also a parabola). A quadratic function is function of the form f ( x ) = ax 2 + bx + c , where a , b and c are constants. For example, if a = 1, b = 0 . 5 and c = 10 then f ( x ) = x 2 + 0 . 5 x + 10. Sometimes you can solve a quadratic equation by factoring. Otherwise you can always solve a quadratic equation using the quadratic formula. Quadratic Formula: If f ( x ) = ax 2 + bx + c , then x =- b ± √ b 2- 4 ac 2 a 1. Solve ( x- 2) 2 = 0. 2. Solve ( x- 2) 2 = 4. 1 3. Solve ( x- 10)( x- 20) = 0. 4. Solve x 2- 7 x + 12 = 0. 5. Solve x 2 + 2 x + 1 = 0. 6. Solve 6 x 2- 5 x + 1 = 0. 7. Solve 5 x 2 + 3 x- 3. 8. Solve x 2 + x + 2 = 0. 9. Suppose you are given ∑ 100 k =1 x 2 = 3455 and ∑ 100 k =1 x = 509. (a) Find ∑ 100 k =1 ( x- 10) 2 . (b) Find ∑ 100 k =1 ( x- ¯ x ) 2 . (c) Find ∑ 100 k =1 ( x- 3) 2 . (d) Find ∑ 100 k =1 ( x- 7) 2 . (e) In which case is the sum the smallest? Provide an explanation. A polynomial function is of the form f ( x ) = a + a 1 x + a 2 x 2 + a 3 x 3 + ... + a n- 1 x n- 1 + a n x n , where a i for i = 1 , 2 , 3 ,...,n are n + 1 constants. The numbers a ,a 1 ,...,a n are called coefficients and n is called the degree of the polynomial. For example, if n = 3 and a i = 2 for all i = 1 , 2 ,...,n then we’d have f ( x ) = 2 + 2 x + 2 x 2 + 2 x 3 , which is a third degree polynomial, which is also called a cubic function. If n = 2 then we have a second degree polynomial, which is also called a quadratic function. If n = 1 then we have first degree polynomial, which is also called a linear function (a straight line!)....
View Full Document

{[ snackBarMessage ]}

Page1 / 13

MATH_REV_PART2_ECO220 - Math Review for ECO220Y PART 2 of 2...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online