Question

Which statement is true about the graph of an exponential decay function in the form y=a(b)x
, where 0<b<1
?(1 point)
Responses

The domain includes all real numbers, the y-intercept is at (0,a)
, and the range includes all real numbers.
The domain includes all real numbers, the y -intercept is at left parenthesis 0 comma a right parenthesis , and the range includes all real numbers.

The domain includes all real numbers, the y-intercept is at (0,a)
, and the horizontal asymptote is at y=0
.
The domain includes all real numbers, the y -intercept is at left parenthesis 0 comma a right parenthesis , and the horizontal asymptote is at y equals 0 .

The y-intercept is at (0,a)
, the range includes all real numbers, and the horizontal asymptote is at y=0
.
The y -intercept is at left parenthesis 0 comma a right parenthesis , the range includes all real numbers, and the horizontal asymptote is at y equals 0 .

The function is always increasing, the y-intercept is at (0,a)
, and the horizontal asymptote is at y=0
.
The function is always increasing, the y -intercept is at left parenthesis 0 comma a right parenthesis , and the horizontal asymptote is at y equals 0 .

Answer 1

The correct statement is: "The domain includes all real numbers, the y-intercept is at (0,a), and the horizontal asymptote is at y = 0."

Reason: b^x is defined for all real x, so domain is all reals; b^0 = 1 gives y(0) = a; and since 0 < b < 1, b^x → 0 as x → ∞, so the graph approaches y = 0 (horizontal asymptote). The function is decreasing (not increasing).