0. Functions

Taxicab fees A taxicab ride costs \$3.50 plus \$2.50 per mile for the first 5 miles, with the rate dropping to \$1.50 per mile after the fifth mile. Let m be the distance (in miles) from the airport to a hotel. Find and graph the piecewise linear function c(m) that represents the cost of taking a taxi from the airport to a hotel m miles away.

Piecewise-Defined Functions

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

a. <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.

c. Find a formula for A(x)

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

Intersection problems Find the following points of intersection.

The point(s) of intersection of the parabolas y= x² and y= -x² + 8x

Which of the following correctly describes the piecewise function graphed below, where the graph consists of a line with slope $2$ for $x<1$ and a constant value $3$ for $x\ge 1$?

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.

a. Find A(2) .

ƒ(t) =6 <IMAGE>

Graphing functions Sketch a graph of each function.

g(x) = { 4-2x if x ≤ 1 , (x-1)² + 2 if x > 1

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.

c. Find a formula for A(x)

ƒ(t) =6 <IMAGE>

Graphing functions Sketch a graph of each function.

ƒ(x) = { 2x if x ≤ 1 , 3-x if x > 1

{Use of Tech} Triple intersection Graph the functions f(x) = x³,g(x)=3^x, and h(x)=x^x and find their common intersection point (exactly).

In Exercises 37 and 38, write a piecewise formula for the function.

<IMAGE>

Piecewise linear functions Graph the following functions.

$f\left(x\right)=\{\begin{array}{c}3x-1\frac{}{},\text{ if }x\le 0\\ -2x-1,\text{ if }x>0\end{array}$

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) =6 <IMAGE>

Roots and powers Sketch a graph of the given pairs of functions. Be sure to draw the graphs accurately relative to each other.

y = (x)¹⸍³ and y = (x)¹⸍⁵