Graph the function $$ f(x)=4^{x-1} $$ by moving the key points. You can only graph integer points, for example you cannot plot the point

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1. The given function is  
   $$
   f(x) = 4^{x-1}.
   $$

2. Recognize that this is a horizontal shift of the basic exponential function $$ 4^x $$. In particular, we can rewrite  
   $$
   f(x) = 4^{x-1} = \frac{4^x}{4}.
   $$
   This shows that compared to $$ 4^x $$, the graph has been shifted to the right by 1 unit.

3. Identify the key integer $$ x $$-values and compute the corresponding $$ y $$-values:

- For $$ x = -1 $$:
     $$
     f(-1) = 4^{-1-1} = 4^{-2} = \frac{1}{16}.
     $$
     So the point is $$( -1, \tfrac{1}{16} )$$.

- For $$ x = 0 $$:
     $$
     f(0) = 4^{0-1} = 4^{-1} = \frac{1}{4}.
     $$
     So the point is $$( 0, \tfrac{1}{4} )$$.

- For $$ x = 1 $$:
     $$
     f(1) = 4^{1-1} = 4^0 = 1.
     $$
     So the point is $$( 1, 1 )$$.

- For $$ x = 2 $$:
     $$
     f(2) = 4^{2-1} = 4^1 = 4.
     $$
     So the point is $$( 2, 4 )$$.

- For $$ x = 3 $$:
     $$
     f(3) = 4^{3-1} = 4^2 = 16.
     $$
     So the point is $$( 3, 16 )$$.

4. Plot these key integer points:  
   - $$( -1, \tfrac{1}{16} )$$
   - $$( 0, \tfrac{1}{4} )$$
   - $$( 1, 1 )$$
   - $$( 2, 4 )$$
   - $$( 3, 16 )$$

5. Connect the points with the smooth curve of an exponential function. The graph will start near zero for very negative $$ x $$ (the function approaches 0 but never touches the $$ x $$-axis) and then increases rapidly as $$ x $$ becomes larger.

Following these steps lets you graph the function $$ f(x) = 4^{x-1} $$ by moving the key points from the basic exponential graph.
Plot the points $$(-1, \frac{1}{16})$$, $$(0, \frac{1}{4})$$, $$(1, 1)$$, $$(2, 4)$$, and $$(3, 16)$$ and connect them with a smooth exponential curve.

Graph the function by moving the key points.
You can only graph integer points, for example you cannot plot the point

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Graph the function by moving the key points. You can only graph integer points, for example you cannot plot the point