f(x)=3^(-2(x+1)) Which of the following equivalent forms of the given function f displays, as the base or the coefficient, the y-coordinate of the y-intercept of the graph of y=f(x) in the xy-plane? A) f(x)=((1)/(3))^((2x+2)) B) f(x)=(1)/(9)((1)/(3))^(2x) C) f(x)=81^((-(1)/(2)x-(1)/(2))) D) f(x)=3^((-2x-2))

Question

f(x)=3^(-2(x+1)) Which of the following equivalent forms of the given function  f displays, as the base or the coefficient, the  y-coordinate of the  y-intercept of the graph of  y=f(x) in the  xy-plane? A)  f(x)=((1)/(3))^((2x+2)) B)  f(x)=(1)/(9)((1)/(3))^(2x) C)  f(x)=81^((-(1)/(2)x-(1)/(2))) D)  f(x)=3^((-2x-2))

Bytelearn · Accepted Answer

Evaluate f(x) at x=0: To find the y-intercept of the graph of y = f(x), we need to evaluate f(x) when x = 0.Substitute x=0 into f(x): Substitute x = 0 into the function f(x) = 3^(-2(x+1)). f(0) = 3^(-2(0+1)) = 3^(-2) = 1/3^2 = 1/9. The y-coordinate of the y-intercept is 1/9.Check options for y-intercept: Now we need to find which of the given options has the y-coordinate of the y-intercept (1/9) as the base or the coefficient.Option A analysis: Option A: f(x) = ((1)/(3))^((2x+2)) can be rewritten as f(x) = (1/3)^(2x+2). This does not have 1/9 as the base or the coefficient.Option B analysis: Option B: f(x) = (1)/(9)((1)/(3))^(2x) has the coefficient 1/9, which is the y-coordinate of the y-intercept.Option C analysis: Option C: f(x) = 81^((-(1)/(2)x-(1)/(2))) can be rewritten as f(x) = (3^4)^(-1/2x-1/2) = 3^(-2x-2), which does not have 1/9 as the base or the coefficient.Option D analysis: Option D: f(x) = 3^((-2x-2)) is the same as the original function and does not have 1/9 as the base or the coefficient.

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