Chapter 7, Problem 28PT

To determine

To graph: the given function, to find the y- intercept and to state the domain and range and the equation of the asymptote.

Explanation of Solution

Given information:

The equation $y=3^x+2$

Concept used:

Domain is the set of input values for which the function is defined.

Range is the set of output values for input values which are in domain.

The y- intercept is the point where the graph crosses the y- axis.

Make a table of values for $y=3^x+2$

$x$	$-10$	$-1$	$0$	$1$	$2$
$y$	$2$	$2.3$	$3$	$5$	$11$

Graph:

The graph of $y=3^x+2$ is shown below.

  

From the graph it is observed that,

y- intercept is $(0,3)$ , Domain is $(-\infty ,\infty )$ , Range is $(2,\infty )$

The horizontal asymptote is $y=2$ and no vertical asymptote.