SOLUTION: g(x)=e^x+3 Description of transformation: Equation(s) from Horizontal Asymptote(s): y-intercept in (x,y) form: I am not sure what this is asking me to do? Help

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: g(x)=e^x+3 Description of transformation: Equation(s) from Horizontal Asymptote(s): y-intercept in (x,y) form: I am not sure what this is asking me to do? Help       Log On


   

Question 147790: g(x)=e^x+3
Description of transformation: Equation(s) from Horizontal Asymptote(s): y-intercept in (x,y) form:
I am not sure what this is asking me to do? Help
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Here's a graph of your equation.
+graph%28+300%2C+300%2C+-5%2C+5%2C+-10%2C+10%2C+2.718%5Ex%2B3%29+
Let me see if I can decipher what you need.
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Horizontal asymptote.
From the equation,
g%28x%29=e%5Ex%2B3
as x becomes large (negative), the exponent term quickly goes to 0,
g%28x%29=0%2B3
g%28x%29=3 as x approaches -infinity
As x goes to negative infinity, the horizontal asymptote is y=3.

It's shown here as the blue line.
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The y intercept in (x,y) form is the point that the graph crosses the y axis.
In that case
x=0 and
g%28x%29=e%5E0%2B3
g%28x%29=1%2B3
g%28x%29=4
In (x,y) format that would be (0,4).

The y-intercept is shown as the green circle.