SOLUTION: I could really use some help graphing these two functions: f(x)=7^x f(x)= log3x

Algebra.Com
Question 173334: I could really use some help graphing these two functions:
f(x)=7^x
f(x)= log3x
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
# 1

In order to graph , we need to plot some points:


Note: I'll use "y" in place of f(x)



Let's find the y value when


Start with the given equation


Plug in


Flip the fraction to make the exponent positive.


Square to get


Divide


So when , then


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


Let's find the y value when


Start with the given equation


Plug in


Flip the fraction to make the exponent positive.


Raise to the first power to get


Divide


So when , then


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


Let's find the y value when


Start with the given equation


Plug in


Raise to the zeroth power to get



So when , then


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


Let's find the y value when


Start with the given equation


Plug in


Raise to the first power to get



So when , then


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


So we have the following values:


xy
-20.02041
-10.14286
01
17




Now let's plot these points





Now draw a curve through those points to graph





Note: the graph does NOT cross or touch the x-axis. It just looks like that since the y values become very small.






# 2



In order to graph , we need to plot some points:


Note: I'll use "y" in place of f(x)


Let's find the y value when


Start with the given equation


Plug in


Use a calculator to evaluate log base 3 of 1 to get 0


So when , then


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



Let's find the y value when


Start with the given equation


Plug in


Use a calculator to evaluate log base 3 of 2 to get 0.63093


So when , then


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



Let's find the y value when


Start with the given equation


Plug in


Use a calculator to evaluate log base 3 of 3 to get 1


So when , then


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



Let's find the y value when


Start with the given equation


Plug in


Use a calculator to evaluate log base 3 of 4 to get 1.26186


So when , then


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


Let's find the y value when


Start with the given equation


Plug in


Use a calculator to evaluate log base 3 of 5 to get 1.46497


So when , then


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




So we have the following values:


xy
10
20.63093
31
41.26186
51.46497




Now let's plot these points





Now draw a curve through those points to graph



RELATED QUESTIONS

I am not understanding these Adavanced Functions and could use some help please.... (answered by stanbon,KMST)
find the composition of functions (fog)(x) for: g(x) = (2x) (1/2), f(x) = x2 + 1 I... (answered by Fombitz)
Graph f(x) =... (answered by jim_thompson5910)
In order to plot the graphs of the following functions, what do I do first? I am so lost! (answered by scott8148)
Dear tutors, I am desperate, I need help plotting and graphing these questions. Any... (answered by Alan3354,solver91311)
I need help ploting and graphing the following equations: f(x)=4x - 3 f(x)=(1/5)x... (answered by Mathtut)
for the function f defined by f(x)=4x^2+5x+9, find the following values: a. f(-2)= b.... (answered by math-vortex)
I could really use some help. Please solve the system of equations by graphing. y =... (answered by solver91311)
I could really use some help on this one. For the function f(x) = x² - 3x + 4 construct... (answered by rapaljer)