Graph f(x)=4^x -5

Question

Graph this lovely function 

 

Answer 1

You should recognize this type of equation as an EXPONENTIAL.  Begin by graphing (or sketching) y = 4^x.  For negative x values, the graph gets lower and lower as x moves farther to the left, but never gets as low as the x-axis. When x = 0, y = 1. Then for x=1, 2, 3, etc. you have y = 4, 16, 64, etc.

 

Now the version you were told to graph is y = 4^x -5...this means that every point you graphed for y = 4^x should be moved down exactly 5 units.

 

YOUR final graph has an HORIZONTAL ASYMPTOTE, the horizontal line y = -5.  Recognizing Exponential functions and their graphs is a fundamental lesson in Algebra 2.  (Pattern recognition being one of the standard skills that math teachers want everyone to acquire.)

Answer 2

Hi Virginia,

 

Let's begin by setting up a table of x, f(x) values.

 

x             f(x)

------------------

0             -5

1             -1

1.1609    ~0 

2             11

3             59

4           251

 

I'll leave the plotting of the graph to you.