Chapter 1.8, Problem 7PPS

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 7PPS

Nonlinear

  $y$ -intercepts: $5$

  $x$ -intercepts: $21$

Symmetry: $x=10$

Positive for $0<x<21$

Negativefor $x>21$

The function increasing for $0<x<10$

The function is decreasingfor $x>10$

Relative Extrema: $(10,55)$

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: The graph intersects the $y$ axis at about $(0,5)$ , so the $y$ -intercept of the graph is about $5$ .

This means that the company spends $\$0$ on advertising the profit will be $\$5,000$

  $x$-intercepts: The graph intercept the $x$ axis at $21$

This means that company spends $\$21,000$ in advertising.

Symmetry: Drawing a vertical line through $x=10$ .The graph does have line symmetry.

Positive: The graph is positive when it is above the $x$ axis which occurs for $0<x<21$ .

This means that the company will make a profit if it spends between $\$0$ and $\$21,000$ on advertising.

Negative: The graph is negative when it is below the $x$ axis which occur for $x>21$ .

This means that the company will make a loss if it spends more than $\$21,000$ on advertising.

Increasing: The graph is rising from left to right so it is increasing for $0<x<10$ .

This means that the profit will increase until advertising expenses reach $\$10,000$

Decreasing: The entire graph is fallingfrom left to right so it isdecreasing for $x>10$ .

This means that the prfit will decrease as advertising expenses go above $\$10,000$

Relative Extrema: The point $(10,55)$ is relatively high point so it is a relative extrema.

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

This means that the profit is decreasing if the company spends more on the advertising.