How do you find the y intercepts for #q(x) = -7^(x-4) -1#?

1 Answer
Jun 15, 2015

Answer:

The y -intercept is at #-(1+1/1401)#
(but see note below).

Explanation:

The y-intercept is where the function crosses the y-axis; for all points on the y-axis, #x=0#.

When #x=0#
#color(white)("XXXX")##g(x)# (also know as #y#) #= -7^(x-4)-1#
#color(white)("XXXX")#becomes
#color(white)("XXXX")##g(0) = -7^-4-1#
#color(white)("XXXX")##color(white)("XXXX")##= - 1/(7^4) -1# see note below
#color(white)("XXXX")##color(white)("XXXX")##= -(1+1/1401)#

note
This assumes #-7^(x-4)# is interpreted as #-(7^(x^4))# and not as #(-7_^(x-4))#. If this is not the case the correct answer would be #-(1-1/1401)#