0. Functions

Using the piecewise function below, evaluate $f\left(5\right)$

Area functions Let A(x) be the area of the region bounded by the t -axis and the graph of y=ƒ(t) from t=0 to t=x. Consider the following functions and graphs.

a. Find A(2) .

ƒ(t) = {-2t+8 if t ≤ 3 ; 2 if t >3 <IMAGE>

Piecewise-Defined Functions

In Exercises 35 and 36, find the (a) domain and (b) range.

𝔂 = { √ -x, -4 ≤ x ≤ 0

{ √ x, 0 < x ≤ 4

Using the piecewise function below, evaluate $$$f\(\left\)(-1\(\right\))$

Piecewise-Defined Functions

Find a formula for each function graphed in Exercises 29–32.

b. <IMAGE>

In Exercises 35 and 36, find the (a) domain and (b) range.

𝔂 = { -x - 2, -2 ≤ x ≤ - 1

{ x, -1 < x ≤ 1

{ -x + 2, 1 < x ≤ 2

Graph the following functions.

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Graphing equations Graph the following equations. 

c. x² + 2x + y² + 4y + 1 = 0

Parabola properties Consider the general quadratic function ƒ(x) = ax² + bx + c , with a ≠ 0.

a. Find the coordinates of the vertex of the graph of the parabola y= ƒ(x)  in terms of a, b, and c.

Piecewise-Defined Functions

Find a formula for each function graphed in Exercises 29–32.

a. <IMAGE>

Piecewise-Defined Functions

Find a formula for each function graphed in Exercises 29–32.

b. <IMAGE>

Area functions Let A(x) be the area of the region bounded by the t -axis and the graph of y=ƒ(t) from t=0 to t=x. Consider the following functions and graphs.

b. Find A(6).

ƒ(t) = {-2t+8 if t ≤ 3 ; 2 if t >3 <IMAGE>

Defining piecewise functions Write a definition of the function whose graph is given <IMAGE>