CK-12-Pre-Calculus Concepts

1.9. Asymptotes and End Behavior http://www.ck12.org 7.y=ln(x) 8.y= 1 +^1 e−x 9. 10. 11. ...

http://www.ck12.org Chapter 1. Functions and Graphs Vertical asymptotes occur atxvalues where a function is not defined. Explai ...

1.10. Continuity and Discontinuity http://www.ck12.org 1.10 Continuity and Discontinuity Here you will learn the formal definiti ...

http://www.ck12.org Chapter 1. Functions and Graphs Jump discontinuitiesoccur when a function has two ends that don’t meet even ...

1.10. Continuity and Discontinuity http://www.ck12.org f(x) =    x^2 − 4 x< 1 − 1 x= 1 −^12 x+ 1 x> 1 Solution: There ...

http://www.ck12.org Chapter 1. Functions and Graphs Describe the discontinuities of the function below. Describe the discontinu ...

1.10. Continuity and Discontinuity http://www.ck12.org 2.y=x^2 3.y=x^3 4.y=√x ...

http://www.ck12.org Chapter 1. Functions and Graphs 5.y=^1 x 6.y=ex 7.y=ln(x) 8.y= 1 +^1 e−x ...

1.10. Continuity and Discontinuity http://www.ck12.org 10. 11. 12.f(x)has a jump discontinuity atx=3, a removable discontinu ...

http://www.ck12.org Chapter 1. Functions and Graphs 1.11 Function Composition Here you will learn a new type of transformation c ...

1.11. Function Composition http://www.ck12.org There are two notations used to describe function composition. In each case the o ...

http://www.ck12.org Chapter 1. Functions and Graphs What isf ( j(h(g(x))) ) ? Solution:These functions arenestedwithin the argum ...

1.11. Function Composition http://www.ck12.org g(x) =ex h(x) =−x Composeg(f(x))and graph the result. Describe the transformatio ...

http://www.ck12.org Chapter 1. Functions and Graphs The positive portion of the exponential graph has been mirrored over theyaxi ...

1.11. Function Composition http://www.ck12.org Practice For questions 1-9, use the following three functions:f(x) =|x|,h(x) =−x, ...

http://www.ck12.org Chapter 1. Functions and Graphs 1.12 Inverses of Functions Here you will learn about inverse functions and w ...

1.12. Inverses of Functions http://www.ck12.org When given a function there are two steps to take to find its inverse. In the or ...

http://www.ck12.org Chapter 1. Functions and Graphs f−^1 (f(x)) =f−^1 ((x+ 1 )^2 + 4 ) =− 1 ± √ ((x+ 1 )^2 + 4 )− 4 =− 1 ± √ (x+ ...

1.12. Inverses of Functions http://www.ck12.org What is the inverse off(x) =y=sinx? Solution:The sine function does not pass the ...

http://www.ck12.org Chapter 1. Functions and Graphs Determine the inverse off(x) =x+x 4. Answers: To find the inverse, y= 5 + ...