The y-intercept of the equation g(x) = 3^x - 5 is (0, -4) and the asymptote of the equation g(x) = 3^x - 5 is y = -5
How to determine the y-intercept?
The equation of the function g(x) is given as:
g(x) = 3^x - 5
The y-intercept is a point on the graph where the value of x is 0
This is represented by x= 0 or (0, y)
This means that we substitute 0 for x in the above equation
So, we have:
g(0) = 3^0 - 5
Evaluate the exponent 3^0
g(0) = 1 - 5
Evaluate the difference of 1 and 5
g(0) = -4
Rewrite this point as
(0, -4)
This means that the y-intercept of the equation g(x) = 3^x - 5 is (0, -4)
How to determine the asymptote?
The equation of the function g(x) is given as:
g(x) = 3^x - 5
The asymptote is a point on the graph where that is parallel to the graph
In the above equation, we have:
g(x) = 3^x - 5
Express the radical as 0
y = 0 - 5
Evaluate the difference of 0 and 5
y = -5
This means that the asymptote of the equation g(x) = 3^x - 5 is y = -5
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