Parent Functions General Forms Transforming linear and quadratic function

Parent Function O The simplest form of any function O Each parent function has a distinctive graph O We will summarize these in the next few slides

Constant Function O f(x)=a; where a is any number

Linear Function O f(x)=x

Absolute Value Function

Quadratic Function O f(x)=x 2

Cubic Function O f(x)=x 3

Rational Functions

Radical Functions

Constant Function O f(x)=a; where a is any number O Domain: all real numbers O Range: a

Linear Function O f(x)=x O Domain: all real numbers O Range: all real numbers

Transformations Linear and Quadratic

Vertical Translations O Positive Shift (Shift up) O Form: y=f(x)+b where b is the shift up O Negative Shift (Shift down) O Form: y=f(x)-b where b is the shift down

Horizontal Translations O Shift to the right O Form: y=f(x-h) O The negative makes you think left, but actually means right here O Shift to the left O Form y=f(x+h) O This would shift to the left of the origin

Vertical Stretch and Compression O If y=f(x), then y=af(x) gives a vertical stretch or compression of the graph of f O If a>1, the graph is stretched vertically by a factor of a O If a<1, the graph is compressed vertically by a factor of a

Horizontal Stretch and Compression O If y=f(x),then y=f(bx) gives a horizontal stretch or compression of the graph of f O If b>1, the graph is compressed horizontally by a factor of 1/b O If b<1, the graph is stretched horizontally by a factor of 1/b

Reflection O If y=f(x), then y=-f(x) gives a reflection of the graph f across the x axis O If y=f(x), then y= f(-x) gives a reflection of the graph f across the y axisl