## 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 $\boxed{\rightarrow}$ ENTER ENTER ( $3$ ) ENTER

See Figure B.43.

### 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).