Chapter 4, Problem 7RE

To determine

To Sketch:The graph of the function $g\left(x\right)=3+2^x$ . State the domain, range and asymptote.

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Answer to Problem 7RE

Explanation of Solution

Given: $g\left(x\right)=3+2^x$

First make the table of $x$ and $y$ by taking random value $x$ .

  $\begin{array}{cccccc}x& -2& -1& 0& 1& 2\\ f\left(x\right)& 3.25& 3.5& 4& 5& 7\end{array}$

Now, plot the points on graph and join the points.

This is exponential function. According to graph, domain is all real number and range is all positive real number.

  $\begin{array}{l}D\in \left(-\infty ,\infty \right)\\ R\in \left(3,\infty \right)\end{array}$

Here, only one horizontal asymptote, $y=3$