Basic Graphs WorksheetBasic Linear Function:f (x) x=Domain:( , )- ��Range:( , )- ��x intercept: (0, 0) y intercept: (0, 0)Increasing everywhere.This function is one-to-one.Example of a shifted graph:3f (x 2) 1+ -- shifting instructions: stretched by 3, left 2, down 1- new formula:y 3x 5= + try to get this yourself by working with the shifting instructions!Domain:( , )- ��Range:( , )- ��x intercept: (-5/3, 0) y intercept: (0, 5)1Basic Quadratic function:2f (x) x=Domain:( , )- ��Range:[0, )�x intercept: (0, 0) y intercept: (0, 0)Decreasing:( ,0)- �Increasing:(0, )�This function is not one-to-one.Example of a shifted graph:f (x 2) 9+ -- shifting instructions: left 2, down 9- new formula:2f (x) x 4x 5= + -Domain:( , )- ��Range:[ 9, )- �x intercepts: (-5, 0) and (1, 0)y intercept: (0, -5) track the key point (0, 0) to (-2, -9)2Basic Cubic function:3x)x(f Domain:),( Range:),( x intercept: (0, 0) y intercept: (0, 0)Increasing everywhere.This function is one-to-one.Example of a shifted graph: ½ f(x - 1)- shifting instructions: shrink by ½, right 1- new formula:3)1x(21)x(f Domain:),( Range:),( x intercept: (1, 0)y intercept: (0, -1/2)track the key point (0, 0) to (1, 0)3Basic Cube Root function:313xx)x(f Domain:),( Range:),( x intercept: (0, 0) y intercept: (0, 0)Increasing everywhere.This function is one-to-one.Example of a shifted graph: f(x + 1) - 2- shifting instructions: left 1, down 2- new formula:2)1x()x(f31Domain:),( Range:),( x intercept: (7, 0) y intercept: (0, -1)track the key point (0, 0) to (-1, -2)4Basic Square Root function:21xx)x(f Domain:[0, )�Range:),0[ x intercept: (0, 0) y intercept: (0, 0)Increasing on its domain.This function is one-to-one.Example of a shifted graph: -f(3 - x)- shifting instructions: reflect about the x axis, left 3, reflect about the y axis- new formula:x3)x(f Domain:]3,(Range:),0[ x intercept: (3, 0)y intercept: )3.0( 5Basic Rational function:1xx1)x(fDomain:),0()0,( Range:),0()0,( x intercept: noney intercept: nonevertical asymptote: x = 0horizontal asymptote: y = 0Decreasing on it’s domainThis function is one-to-one.Example of a shifted graph: f(x + 2) - 3- shifting instructions: left 2, down 3- new formula:5 3xf (x)x 2- -=+ try to get this yourself by working with the shifting instructions!Domain:),2()2,( Range:),3()3.( x intercept: (5/3, 0)y intercept: (0, 5/2)vertical asymptote: x = -2horizontal asymptote y = -3Track the key point (1, 1) to (-1, -2).6Basic Absolute Value function:x)x(f Domain:),( Range:),0[ x intercept: (0, 0) y intercept: (0, 0)Decreasing:( ,0)- �Increasing:(0, )�This function is not one-to-one.Example of a shifted graph: -f(x - 5) +2- shifting instructions: reflect about the x axis, right 5, up 2- new formula:25x)x(f Domain:),( Range:]2,(x intercepts: (7, 0) and (3, 0) y intercept: (0, -3)7Basic exponential function:xf (x) b b 1,0= �Domain:),( Range:(0, )�x intercept: none y intercept: (0, 1)horizontal asymptote: y = 0Increasing everywhere.(illustration is with b = 3)Example of a shifted graph: -f(x + 3) + 9- shifting instructions: reflect about the x axis, left 3, up 9,- new formula:x 3f (x) 3 9+=- +Domain:),( Range:( ,9)- �x intercept: (-1, 0)y intercept: (0, -18)horizontal asymptote: y = 9Be sure to know how to handle thisif b = e.8Basic logarithmic function:Domain:(0, )�Range:( , )- ��x intercept: (0, 1) y intercept: noneVertical asymptote: x = 0Increasing everywhere.This function is 1:1.(illustration is with b = 10)Example of a shifted graph:- shifting instructions: left 2, reflect y- new formula:f (x) log(2 x)= - try to get this yourself by working with the shifting instructions!Domain:( ,2)- �Range:( , )- ��x intercept: (1, 0) y intercept:(0,log 2)vertical asymptote: x =