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Graphing Logarithmic Functions

Question 4 • FL-1200330-Algebra 2 CR

Consider f(x) = bx. Which statement(s) are true for 0 < b < 1? Check all that apply.

Answer
A
The domain is all real numbers.
B
The domain is x > 0.
C
The range is all real numbers.
D
The range is y > 0.
E
The graph has x-intercept 1.
F
The graph has a y-intercept of 1.
G
The function is always increasing.
H
The function is always decreasing.

Explanation

For the exponential function f(x) = b^x, every real x is allowed, so the domain is all real numbers. Its values are always positive, and f(0) = b^0 = 1, giving range y > 0 and a y-intercept of 1. When 0 < b < 1, increasing x makes b^x smaller, so the function is always decreasing.

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