Chapter 9.4, Problem 33E

To determine

To calculate: To sketch the curve represented by the parametric equations using graphing utility and then use the graph and Vertical line test to determine whether $y$ is function of $x$

Answer to Problem 33E

  $y$ is function of $x$

Explanation of Solution

Given information: Parametric equations are

  $\begin{array}{l}x=\frac{t}{2}\\ y=\ln \left(t^2+1\right)\end{array}$

Formula Used:

The Vertical Line Test is used to determine whether a graph represents a function. When any vertical line intersects the graph more than once, then graph does not define a function because that $x$ value has more than one output

Calculation:

Parametric equations are given as

  $\begin{array}{l}x=\frac{t}{2}\\ y=\ln \left(t^2+1\right)\end{array}$

Sketching the graph using graphing utility as follows:

  

Vertical Line test:

  

Since the vertical line intersects the graph only once

Thus, $y$ is function of $x$

Conclusion:

Hence, $y$ is function of $x$