I need to write 2 equations that represent the same exponential function with a y-intercept of 5 and an asymptote at y=3. I got y=2^(x+1) + 3 but I don't know how to find the second equation. Can someone please explain this to me. Thanks.
To find the second equation that represents the same exponential function with a y-intercept of 5 and an asymptote at y=3, we need to manipulate the given equation in a way that preserves these properties.
The given equation is: y = 2^(x+1) + 3
To modify this equation, we will use algebraic operations to shift the graph vertically. This will allow us to change the y-intercept while keeping the shape and slope intact.
To achieve a y-intercept of 5, we need to raise the entire function by 2 units. This can be done by adding 2 to the equation, resulting in:
y = 2^(x+1) + 3 + 2
Simplifying this equation, we get:
y = 2^(x+1) + 5
So, the modified equation is y = 2^(x+1) + 5, which represents the same exponential function as the given equation but with a y-intercept of 5.