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Q. 55

Expert-verified
Found in: Page 284

Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

Begin with the graph of $y={e}^{x}$and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.$f\left(x\right)={e}^{x+2}$

The graph of the function is given below,

Domain: All real numbers.

Range: $\left\{y|y>0\right\}or\left(0,\infty \right)$

Horizontal asymptote: $y=0$

See the step by step solution

Step 1. Given information.

Consider the given function,

$f\left(x\right)={e}^{x+2}$

First, plot the graph of $y={e}^{x}$. Then add $2$ and shift up by $2units$,

Step 2. Determine the characteristics of the function.

Consider the given function,

$f\left(x\right)={e}^{x+2}$

From the graph, the domain of the function is all real numbers.

The range is $\left\{y|y>0\right\}$ or in the interval $\left(0,\infty \right)$.

Horizontal asymptote is $y=0$.