Questions: Graph the function. y=3^(2x+2)+1 Specify the domain, range, intercept(s), and asymptote. (If an answer does not exist, enter DNE.)

Transcript text: Graph the function. \[ y=3^{2 x+2}+1 \] Specify the domain, range, intercept(s), and asymptote. (If an answer does not exist, enter DNE.)

Solution

Solution Steps

Step 1: Identify the correct graph

The given function is $y = 3^{2x+2} + 1$. This is an exponential function of the form $y = ab^x + c$, where $a=1$, $b=3^2=9$, and $c=1$. The base is 9, which is greater than 1, so the graph should be increasing. The graph should also have a horizontal asymptote at $y = c = 1$. The third graph from the top left satisfies these properties.

Step 2: Find the domain

The domain of an exponential function is all real numbers.

Step 3: Find the range

Since the base of the exponential function is greater than 1, and the vertical shift is 1, the range of the function is $(1, \infty)$.