Question

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

$\mathit{y}\mathbf{=}{\mathbf{4}}^{\mathbf{x}}\mathbf{+}\mathbf{2}$

Short answer

The graph of the function is:

$\mathit{y}$-intercept is $\mathbf{(}\mathbf{0}\mathbf{,}\mathbf{3}\mathbf{)}$and domain is all real number and range is $\mathit{y}\mathbf{>}\mathbf{3}$.

Step-by-step solution

Step 1. Graph the equation.

Graph of the function:$y=4^x+2$

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.

$y=4^x+2$

$\begin{array}{l}y=4^x+2\\ =4^0+2[x=0]\\ =1+2\\ =3\end{array}$

Thus, $y$–intercept is $y=3$.

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$y>3$.