Chapter 1.8, Problem 10PPS

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 10PPS

Nonlinear

  $y$ -intercepts: $0$

  $x$ -intercepts: $0$

No Symmetry

Positive for all real numbers.

The function is not negative

The function increasing forall 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: $y$ -intercept of the graph is about $0$ .

  $x$-Intercepts: $x$-interceptsof the graph is about $0$ .

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 swing is always positive.

Negative: The graph is not negative

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

This means that swing is always increasing.

Decreasing: The function is not decreasing.

Relative Extrema:There is no relative high or low point.

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

This means that length of pendulum increases, the swing time increases.