Chapter 1.8, Problem 12PPS

To determine

Tofind:Key features of the graph.

Answer to Problem 12PPS

Nonlinear

  $y$ -intercept= $0$

  $x$-intercepts at every multiple of $4$ .

Relative maximum = $2$

Relative minimum= $6$

The graph bounces between 1 $25$ And3

  $-25$ .

Explanation of Solution

Given: At the beginning of the Ferris wheel ride, a passenger cart is located at the same height as the center of the wheel. The position $y$ in feet of this cart relative to the center $t$ seconds after the ride starts is given by the function graphed at the right. Identify and interpret the key features of the graph.

  

Linear or Nonlinear: Since the graph is a curve, not a line. The graph is Nonlinear.

  $y$-Intercepts: $y$ -intercept of the graph is about $0$ .

  $x$-intercepts: The graph has $x$-intercepts at every multiple of $4$ .

This means that the height will be same as the height of the center of the wheel every $4$ seconds.

The graph has a relative maximum at $2$ and then repeats every $8$ seconds.

The graph has a relative minimum at $6$ and then repeats every $8$ seconds.

The graph bounces between $25$ and $-25$ .