SOLUTION: Graph the following. Label all x-intercepts, y-intercepts, and any asymptotes. {{{f(x)=2^x-4}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Graph the following. Label all x-intercepts, y-intercepts, and any asymptotes. {{{f(x)=2^x-4}}}      Log On


   

Question 130693: Graph the following. Label all x-intercepts, y-intercepts, and any asymptotes.


f%28x%29=2%5Ex-4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph f%28x%29=2%5Ex-4, we need to plot some points. To do that, we need to plug in some x values to get some y values


So let's find the first point:



f%28x%29=2%5Ex-4 Start with the given function


f%280%29=2%5E%280%29-4 Plug in x=0


f%280%29=1-4 Raise 2 to the 0th power to get 1


f%280%29=-3 Subtract 4 from 1 to get -3


So when x=0, we have y=-3


So our 1st point is (0,-3)


-------------- Let's find another point --------------


f%28x%29=2%5Ex-4 Start with the given function


f%281%29=2%5E%281%29-4 Plug in x=1


f%281%29=2-4 Raise 2 to the 1st power to get 2


f%281%29=-2 Subtract 4 from 2 to get -2


So when x=1, we have y=-2


So our 2nd point is (1,-2)


-------------- Let's find another point --------------


f%28x%29=2%5Ex-4 Start with the given function


f%282%29=2%5E%282%29-4 Plug in x=2


f%282%29=4-4 Raise 2 to the 2nd power to get 4


f%282%29=0 Subtract 4 from 4 to get 0


So when x=2, we have y=0


So our 3rd point is (2,0)


-------------- Let's find another point --------------


f%28x%29=2%5Ex-4 Start with the given function


f%283%29=2%5E%283%29-4 Plug in x=3


f%283%29=8-4 Raise 2 to the 3rd power to get 8


f%283%29=4 Subtract 4 from 8 to get 4


So when x=3, we have y=4


So our 4th point is (3,4)


-------------- Let's find another point --------------


f%28x%29=2%5Ex-4 Start with the given function


f%284%29=2%5E%284%29-4 Plug in x=4


f%284%29=16-4 Raise 2 to the 4th power to get 16


f%284%29=12 Subtract 4 from 16 to get 12


So when x=4, we have y=12


So our 5th point is (4,12)


Now lets make a table of the values we have calculated 



 xy



 0-3
 

 1-2
 

 20
 

 34
 

 412
Now plot the points



Now connect the points to graph y=2%5Ex-4 (note: the more points you plot, the easier it is to draw the graph)



By looking at the graph, we can note the following


x-intercept: (2,0)

y-intercept: (0,-3)

Horizontal Asymptote(s): y=-4 (ie a horizontal line at the y value of -4)

Vertical Asymptote(s): none (ie the graph continues on forever in both directions along the x-axis)