# Modeling, Functions, and Graphs

## SectionB.7Function Notation and Transformation of Graphs

### SubsectionFunction Notation

The calculator uses $$Y_1 (X)\text{,}$$ $$Y_2 (X)\text{,}$$ and so on, instead of $$f (x)\text{,}$$ $$g(x)\text{,}$$ and so on, for function notation.

#### ExampleB.42.

Evaluate $$f (x) = x^2 + 6x + 9$$ for $$x = 3\text{.}$$
1. Set $$Y_1 = X^2 + 6X + 9\text{,}$$ and quit (2nd MODE) to the Home screen.
2. To evaluate this function for $$X = 3\text{,}$$ press
VARS ENTER ENTER ( $$3$$ ) ENTER

### SubsectionTransformation of Graphs

We can use function notation to facilitate graphing transformations. In the examples below, we use $$f (x) = x^2\text{.}$$

#### SubsubsectionTranslations

##### ExampleB.44.
Compare the graphs of $$y = f (x) - 8$$ and $$y = f (x - 8)$$ with that of $$y = f (x)\text{.}$$
Define $$Y_1 = X^2$$ and $$Y_2 =Y_1(X) - 8$$ . Press ZOOM $$6$$ to see the graphs (Figure B.45).
Define $$Y_1 = X^2$$ and $$Y_2 =Y_1(X - 8)\text{.}$$ Press ZOOM $$6$$ to see the graphs (Figure B.46).

#### SubsubsectionVertical Scalings and Reflections

Compare the graph of $$y = \frac{-1}{2} f (x)$$ with that of $$y = f (x)\text{.}$$
Define $$Y_1 = X^2$$ and $$Y_2 = -1/2*Y_1(X)\text{.}$$ Press to see the graphs (Figure B.47).