Given:
[tex]y=(\frac{1}{4})^x[/tex]
Required:
Translate it to the graph of
[tex]y=(\frac{1}{4})^{x-1}-2[/tex]
Explanation:
Rewrite the function as:
[tex]\begin{gathered} y=(\frac{1}{4})^x(\frac{1}{4})^{-1}-2 \\ y=4(\frac{1}{4})^x-2 \end{gathered}[/tex]
To graph the function
[tex]y=4(\frac{1}{4})^x[/tex]
multiply all the y- coordinates of the function
[tex]y=(\frac{1}{4})^x[/tex]
by 4. Since 4>1, so the graph has a vertical stretching.
The graph of
[tex]y=4(\frac{1}{4})^x-2[/tex]
shift the graph of
[tex]y=4(\frac{1}{4})^x[/tex]
2 units down by subtracting 2 from the y-coordinate of the points of the graph
[tex]y=4(\frac{1}{4})^{x}[/tex]
Thus the graph of
[tex]y=(\frac{1}{4})^{x-1}-2[/tex]
Final Answer:
