# How do you graph, find the intercepts and state the domain and range of f(x)=4^x+3?

Jul 14, 2018

The domain is $\mathbb{R}$ . The range is $y \in \left(3 , + \infty\right)$

#### Explanation:

The function is

$f \left(x\right) = {4}^{x} + 3$

The graph is as follows

graph{4^x+3 [-19.06, 26.55, -3.99, 18.83]}

The domain is $\mathbb{R}$ as $\forall x \in \mathbb{R} , \exists y$

And,

${\lim}_{x \to - \infty} f \left(x\right) = {\lim}_{x \to - \infty} {4}^{x} + 3 = 3$

${\lim}_{x \to + \infty} f \left(x\right) = {\lim}_{x \to + \infty} {4}^{x} + 3 = + \infty$

The range is $y \in \left(3 , + \infty\right)$