# 004 Sample Final A, Problem 5

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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
1) What is the basic graph of $f(x)=3^{(x+1)}-2$ ?
2) How is the graph $g(x)=x+1$ obtained from $f(x)=x$ ?
3) How is the graph $g(x)=(x-3)^{2}$ obtained from $f(x)=x^{2}$ ?
1) The basic graph is $y=3^{x}$ .
2) The graph of $g(x)$ is obtained by shifting the graph of $f(x)$ up 1 unit.
3) The graph of $g(x)$ is obtained by shifting the graph of $f(x)$ to the right by 3 units.

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 $y=-2$ .
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 $y=-2$ 