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

Question

𝑦
=
𝑎
(
𝑏
)
𝑥
, where 0<b<1
0
<
𝑏
<
1
?(1 point)
Responses

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

Answer 1

For an exponential decay function in the form \( y = a(b)^x \), where \( 0 < b < 1 \):

1. The function is always decreasing, not increasing, as \( x \) increases.
2. The y-intercept is at \( (0, a) \).
3. The domain includes all real numbers (\( (-\infty, \infty) \)).
4. The range includes all real numbers greater than 0 (\( (0, \infty) \)), but not all real numbers because the output will never reach 0.

Thus, the correct statement about the graph of this function would be:

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

So the last response option is the correct one.