Question

2. Determine the equation of the asymptote for the following exponential functions: *y=2x-3 b. y = (3)* + 2 c. ** y = 2(3)* d. 2 + 3x I *** a.

Answer 1

a) y = -3

b) y = 2

c) y = 0

d) y = 2

Explanation:

The asymptote is the constant added to the expression of the variable

a) y = 2^x - 3

Theexpression of the variable = 2^x

The number after it is is - 3

So the asymptote is y = -3

b) y = (1/3)^x + 2

The number added to the expression of the variable is 2

Asymptote is y = 2

c) y = 2(3)^x

y = 2(3)^x + 0

The expression of the variable = 2(3)^x

There is no number added to the expression of the variable

Hence, Asymptote is y = 0

d) 2 + 3^x

$\begin{gathered} The\text{ function is not equated to y} \\ Since\text{ we are told they are all exponntial function,} \\ \text{let 2 + 3}^x\text{ = y} \end{gathered}$

The expression of the variable = 3^x

The number added to this expression is 2

Asymptote is y = 2