Chapter 1.8, Problem 8PPS

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 8PPS

Nonlinear

  $y$ -intercepts: $200$

No $x$ -intercepts

No Symmetry

Positive for all real numbers.

The function is not negative

The function increasing for all real numbers.

The function is not decreasing

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 a curve, not a line. The graph is Nonlinear.

  $y$-intercepts: The graph intersects the $y$ axis at about $(0,200)$ , so the $y$ -intercept of the graph is about $200$ .

This means that initial number of hits is about $200$

  $x$-intercepts: No $x$-intercepts

This means that the number of hits will never be zero.

.

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 number if hits is always positive.

Negative: The graph is not negative

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

This means that the number of hits is always increasing.

Decreasing: The entire graph is risingfrom left to right so it is not decreasing.

Relative Extrema: No relatively low or high points.

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

This means that the number of hits is increasing.