18
QuizMultiple Choice

Graphing Logarithmic Functions — Quiz

Question 18 • Algebraic Reasoning

Which properties are present in a table that represents a logarithmic function in the form y is equal to the log base b of x when b is greater than 1 ? I The y -values are always increasing or always decreasing. II The point open paren 0 comma 1 close paren exists in the table. III The y -values will decrease rapidly as the x -values approach zero. IV There will only be one x -value in the table with a y -value of zero.

Answer
A
I, III, and IV
B
I and II only
C
I only
D
II and III only

Explanation

For b > 1, y = log_b(x) is increasing, so its y-values always increase as x increases (I). As x approaches 0 from the positive side, the logarithm decreases without bound (III). The graph does not include (0, 1), since x = 0 is outside the logarithm’s domain; and y = 0 occurs only when x = 1, so IV is also true. Therefore, the correct choice is A, I, III, and IV.

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