004 Sample Final A, Problem 5

Describe how the graph of $f(x)=3^{(x+1)}-2$  can be obtained from a basic graph. Then sketch the graph. Provide at least two ordered pairs, and the equation of any asymptote.

Foundations
Answer:

Solution:

Step 1:
We start with the basic graph of $g(x)=3^{x}$.
To get the graph of $f(x)$ from $g(x)$, we shift the graph of $g(x)$ down 2 and to the left by 1.

Step 2:
Two ordered pairs are (-1,-1), and (0,1). There is a horizontal asymptote at $y=-2$.

Final Answer:
To get the graph of $f(x)$ from $3^{x}$, we shift the graph of $3^{x}$ down 2 and to the left by 1.
Two ordered pairs are (-1,-1), and (0,1). There is a horizontal asymptote at $y=-2$

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