CPM Homework Help : CALC Problem 1-21

Given the following functions, compute the given values.

$f ( x ) = \left\{ \begin{array} { c c c } { 4 - 3 x } & { \text { for } } & { x \leq 1 } \\ { x ^ { 2 } } & { \text { for } x > 1 } \end{array} \right.$

Find $f (0)$ , $f (1)$ , and $f (3)$ .

$f ( x ) = \left\{ \begin{array} { c c } { \sqrt { x } } & { \text { for } x < 3 } \\ { 3 - x } & { \text { for } x \geq 3 } \end{array} \right.$

Find $f (1)$ , $f (3)$ , and $f (9.4)$ .

$f ( x ) = \left\{ \begin{array} { l l l } { - x } & { \text { for } } & { x \leq 0 } \\ { \frac { 5 } { x } } & { \text { for } } & { 0 < x \leq 1 } \\ { 6 - 2 x } & { \text { for } } & { x > 1 } \end{array} \right.$

Find $f (−3)$ , $f (0)$ , $f (0.5)$ and $f (4)$ .

Sketch a graph of $f(x)$ in part (c) above.

Hint (a):

$x = 1$ can be called, informally, the Boundary Point of the piecewise function $f(x)$ . This is because $x ≤ 1$ is the location where the left and the right pieces switch.

More Help (a):

$f(0)$ and $f(1)$ are on the left side of the Boundary Point, $f(3)$ is on the right side of the Boundary Point.

Answer (a):

$f(0) = 4 - 3(0) = 4$ LEFT PIECE
$f(1) = 4 - 3(1) = 1$ LEFT PIECE
$f(3) = (3)^² = 9$ RIGHT PIECE

Hint (b):

The Boundary Point is $x ≥ 3$ . So $f(1)$ lies on the left side of the piecewise function while $f(3)$ and $f(9.4)$ lie on the right.

Hint (c):

This function has two boundary points and three pieces: a left piece, a middle piece and a right piece. On which piece do the points $f(-3)$ , $f(0)$ , $f(0.5)$ and $f(4)$ lie?

Answer (d):