Question

What are the domain,range, and asymoptote of h(x) = (1.4)x + 5

Answer 1

`h(x)=1.4^x+5`


`\text{The domain:}\ x\in\mathbb{R}\\\\\text{The range of}\ y=1.4^x\ \text{is}\ \mathbb{R^+}\\\\h(x)=1.4^x+5\to\text{shift the graph of}\ y=1.4^x\ \text{5 units up}\\\\\text{therefore the range of}\ h(x)=1.4^x+5\ \text{is}\ (5;\ \infty)`


`\text{The horizontal asymptote of}\ y=1.4^x\ \text{is}\ y=0,\\ \text{therefore the asymptote of}\ h(x)=1.4^x+5\ \text{is}\ y=5.`