Chapter 1.8, Problem 9PPS

To determine

Tofind:Function graphed as linear or nonlinear,intercepts,any symmetry,positive and negative, increasing or decreasing,end behavior of the graph.

Answer to Problem 9PPS

Nonlinear

  $y$ -intercepts: $0$

No $x$ -intercepts

No Symmetry

Positive for all real numbers.

The function is not negative

The function increasing for $0<x<8$

The function is decreasing for $x>8$

Relative Extrema: $x=8$

End Behavior: $x$ increases the value of $y$ decreases

Explanation of Solution

Given: Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph, any symmetry, where the function is symmetry, where the function is positive and negative, increasing or decreasing, the $x$ coordinate of any relative extrema, and the end behavior 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 $0$ .

This means there is no medicine in blood when we start measuring.

  $x$-intercepts: No $x$-intercepts

Symmetry: The graph does not have line symmetry.

Positive: The graph is positive when it is above the $x$ axis which occurs for all real numbers.

This means that the after taking the medicine there is always some amount of medicine in blood.

Negative: The graph is not negative

Increasing: The graph is rising from left to right so it is increasing for $0<x<8$

This means that the concentration of medicine increases after first $8$ hours.

Decreasing: The function is decreasing for $x>8$ .

This means that the after eight hours the concentration of the medicine decreases.

Relative Extrema:The relative maximum is about $x=8$ which means that the concentration of medicine is maximum of about $2.5mg/ml$ .

End Behavior: As $x$ increases the value of $y$ decreases.

This means that concentration of medicine become less as the time goes, until there is none left in the blood.