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1. 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

   Read more about asymptote at:

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