Question

function y = b^x (0 < b < 1)
the range of an
exponential function is
all real numbers
positive real numbers
the graph of an exponential function has
a y - intercept only
the graph is
t h r o u g h o u t its domain
and has
at the x - axis because
the value b^x can get very close to 0 but never
reach it.
(there is also a graph of an exponential function curve in the image)

Explanation:

Step1: Analyze the graph's behavior

The graph is an exponential function (since it has the shape of \( y = b^x \) with \( 0 < b < 1 \), decreasing). For exponential functions \( y = b^x \) (\( b>0, b
eq1 \)):

• The domain is all real numbers. The graph is decreasing throughout its domain (as \( b \) is between 0 and 1, so as \( x \) increases, \( y \) decreases).
• The \( x \)-axis is a horizontal asymptote, so the graph has no \( x \)-intercept (since \( b^x = 0 \) has no solution; \( b^x \) approaches 0 but never reaches it).

Step2: Fill in the blanks

First blank (behavior of graph throughout domain): Since \( 0 < b < 1 \), the function is decreasing. So "decreasing".
Second blank (x - intercept): The graph approaches the x - axis but never crosses it, so it has "no x - intercept".

Answer:

First blank: decreasing; Second blank: no x - intercept