Transformation-Shifts

Transformation-Shifts

Vertical ShiftU2.8.2

Vertical ShiftWhen a constant value is added to a function, the graph undergoes a vertical shift.A Vertical Shift is a type of translation that moves the graph up or down depending on the value added to the function

TranslationsA translation of a graph moves the graph either vertically, horizontally, or both, without changing its shape. A translation is sometimes called a slide! A translation is a specific type of transformation

The k elementVertical translations can be performed on linear and exponential graphs using f(x) + kA vertical shift moves the graph up or down k unitsPositive k , +k the graph is translated up k unitsNegative k, -k the graph is translated down k units

2 functions!Given the graphs of two functions that are vertical translation of each other, the value of the vertical shift, k, can be found by finding the distance between the y-intercepts

f(x)=3xh(x)= 3x+2g(x)= 3x+1q(x)= 3x - 1

What is the y-intercept of f(x)? g(x)? h(x)? q(x)?f(x) is 0; g(x) is 1; h(x) is 2; q(x) is -1How can you describe the translation of h(x) from f(x)?shifted up 2 units so k=+2How could you describe the translation of q(x) from f(x)? shifted down 1 unit so k= -1How could you describe the translation of q(x) from g(x)?

Exponential function

Practice time!!!

Practice on worksheet 446-450