Question

Graph each function. Find the y-intercept, and state the domain and range.

$\mathit{y}\mathbf{=}{\mathbf{3}}^{\mathbf{x}}\mathbf{+}\mathbf{1}$

Short answer

The graph of the function is:

$\mathit{y}$-intercept is $\mathbf{(}\mathbf{0}\mathbf{,}\mathbf{2}\mathbf{)}$ and domain is all real number and range is $\mathit{y}\mathbf{>}\mathbf{1}$.

Step-by-step solution

Step 1. Graph the equation.

Graph of the function: $y=3^x+1$

Step 2. Find the y-intercept.

The $y$-intercept of a graph is the point where the graph intersects the $y$-axis that is., $x$-coordinate of a $y$-intercept is 0. So, to find $y$-intercept substitute 0 for $x$into the equation.

$y=3^x+1$

role="math" localid="1647773697046" $\begin{array}{l}y=3^x+1\\ =3^0+1[x=0]\\ =1+1\\ =2\end{array}$

Thus, $y$–intercept is $y=2$.

Step 3. Find the range and domain.

The domain of a function$f\left(x\right)$ is the set of all values for which the function is defined, and the range of the function is the set of all values that $f$ takes.

From the graph, it can be concluded that domain is all real number and range is $y>1$.