Question

Follow this link to view Juan’s work. Critique Juan’s work by justifying correct solutions and by explaining any errors he made. For any errors made, provide and explain a correct response. Be sure to explain each key aspect of the graph.
http://media.education2020.com/ContentEngine/Common//pdfs/3109/3109-07-01/3109-07-01-ShortWritingAssignment.pdf

Answer 1

According to Juan following are the key aspects of the graph shown above in the short assignment.
1) Initial value: –3
2) Base: 3
3) Asymptote: x = 0
4) Domain: {x | x > 0}
5) Range: {y | all real numbers} 
Now,
Correction:
The general foam of exponential function is y=a*bˣ 
Here,
a is the initial value
b is the base
For 1) and 2)
Initial Value & Base:
From the graph(given in the link), choose two points which you can clearly see on the graph.
The two points which I have chosen are (1,3),(2,9) 
Put these points one by one in the above equation which is y=a*bˣ 
For point (1,3)
eq. becomes 3=a*b------1
For point (2,9)
eq. becomes 9=a*b²------2
from eq. 1 you get 3/b=a put it in eq. 2
you get 
9=3/b * b²
from this b=3  so base is equal to 3.(so Juan inspection is correct)

For 'a' put b=3 in eq. 1
So, 3=3*a
a=1 so initial value is equal to 1.(so Juan inspection is wrong)

3) 
Asymptote:
From analytical geometry, you know that an "asymptote" of a curve is a line such that the distance between the curve and line approaches zero.
From the graph(given in link) you can clearly see that only horizontal asymptote exist and also there is no transformation so
Asymptote is y=0 (a horizontal x-axis line).( so Juan inspection is wrong)

4)
Domain:
As we know that domain is the set of all possible inputs for the function and you can clearly see from the graph(in the given link) that you can put any value of x.
So, 
Domain is from negative infinity to positive infinity.
Domain={x| x is from negative infinity to positive infinity}.( so Juan inspection is wrong)

5)
Range:
From the eq. y=a*bˣ you can clearly see that when ever you put negative number in place of x( b⁻ˣ = 1/b) it will always give you positive number.
So,
Range is from 0 to positive infinity, not including zero.
Range={ y| y is from 0 to positive infinity, not including zero}. (so Juan inspection is wrong).