meredith48034
contestada

given the functon g(x)= (1/4)^x, determine the y-intercept and the equation of the asymptote.

a. the y-intercept is (0, 0.25) and the asymptote is at y=0
b. the y-intercept is (1,0) and the asymptote is at y=0. the y-intercept is (1,0) and the asymptote is at y=1
c. the y-intercept is (0,1) and the asymptote is at y=0
d. the y-intercept is (1,1) and the asymptote is at y= 1.

Respuesta :

Ferraz
Hello.

The y-intercept is the point where  x = 0.

Therefore, let us make this in the function.

g(0) = (1/4) ^ 0

g(0) = 1.

The y-intercept is in (0, 1).

To calculate the asymptote, we will take the limit when x→∞.

  lim    (1/4)^x
x→+∞

We know that this limit is 0 because 1/4 < 1, so the powers of (1/4) will decrease as x grows.

The asymptote is, therefore, at y = 0.

Alternative C