Chapter 1.8, Problem 6PPS

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 6PPS

Linear

  $y$ -intercepts: $-400$

  $x$ -intercepts: $4$

No Symmetry

Positive for $x>4$

Negativefor $x<4$

The function increasing for all real numbers

The function is not decreasing anywhere

No relative Extrema

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

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 not a curve , the graph is linear.

  $y$-intercepts: The graph intersects the $y$ axis at about $(0,-400)$ , so the $y$ -intercept of the graph is about $-400$ .

This means that the initial expense is about $\$400$

  $x$-intercepts: The graph intercept the $x$ axis at $4$

This means that the after $4$ weeks, the profit will be $\$0$

Symmetry: The graph does not any symmetry.

Positive: The graph is positive when it is above the $x$ axis which occurs for $x>4$ .

Negative: The graph is negative when it is below the $x$ axis which occur for $x<4$ .

Increasing: The entire graph is rising from left to right so it is increasing for all real numbers.

Decreasing: The entire graph is rising from left to right so it is not decreasing anywhere.

Relative Extrema: There is no high or low point on the graph so the graph does not have any relative extrema.

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

This means that the profit is increasing.