Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson

Chapter 4 - Exponential and Logarithmic Functions - Section 4.3 Exponential Functions - 4.3 Assess Your Understanding - Page 306: 37

Answer

$A$

Work Step by Step

In order to find out the correct answer, we must follow the following points: (a) If the function has a horizontal asymptote of $y=a$ and is below the asymptote, this shows the equation has the form of: $y=m-3^n$. (b) If the function has a horizontal asymptote of $y=a$ and is above the asymptote, this shows the equation has the form of: $y=m+3^n$. (c) The graph of $y=f(x-h)$ represents a horizontal shift, when $h \gt 0$, of $|h|$ units to the right and to the left when $h\lt 0$ of the original function $f(x)$. (d) The exponent of $3$ is positive when the graph is increasing, and it is negative when the graph is decreasing. So, we can see from the depicted graph that the function is $y=3^{x}$ and has a horizontal asymptote of $x=0$. It is positive (above the horizontal asymptote) and increasing. Therefore, $A$ is the correct answer.

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