Which statement is true about the graph of an exponential decay function in the form y=a(b)x

Question

, where 0<b<1
?(1 point)
Responses

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 .

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

Answer 1

The correct statement about the graph of an exponential decay function in the form \( y = a(b)^x \), where \( 0 < b < 1 \), is:

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

This is because:

• The function is defined for all real values of \( x \), making the domain all real numbers.
• The y-intercept, found by evaluating the function at \( x = 0 \), is \( y = a(b)^0 = a \).
• As \( x \) approaches infinity, \( y \) approaches 0, giving the horizontal asymptote at \( y = 0 \).

Thus, this response accurately describes the properties of the graph of an exponential decay function.