Logarithmic Functions Mastery

What is the basic shape of the graph of the logarithmic function y = log(x)?

• A straight line

• A parabola

• An exponential curve

• An increasing curve that approaches the y-axis but never crosses it

What is the domain of the logarithmic function f(x) = log(x)?

• All real numbers

• All positive real numbers

• All negative real numbers

• All real numbers except zero

What is the range of the logarithmic function f(x) = log(x)?

• All real numbers

• All positive real numbers

• All negative real numbers

• All real numbers except zero

If the function f(x) = log_b(x) is graphed, what is the x-coordinate of the y-intercept?

• 0

• 1

• b

• There is no y-intercept

How does the graph of y = log_b(x) change as the base b increases?

• The graph stretches vertically

• The graph compresses vertically

• The graph stretches horizontally

• The graph compresses horizontally

What is the inverse function of y = log_b(x)?

• y = b^x

• y = x^b

• y = 1/b^x

• y = 1/log_b(x)

If f(x) = log_b(x) and g(x) = b^x, which statement is true?

• f(x) and g(x) are the same function

• f(x) and g(x) are inverse functions

• f(x) and g(x) have no relationship

• f(x) is the derivative of g(x)

What happens to the graph of the logarithmic function y = log_b(x) as x approaches zero?

• The graph approaches positive infinity

• The graph approaches negative infinity

• The graph levels off to a horizontal line

• The graph crosses the y-axis

Which of the following transformations will shift the graph of y = log(x) to the left by 3 units?

• y = log(x + 3)

• y = log(x - 3)

• y = log(x) + 3

• y = log(x) - 3