Understanding Logarithmic and Exponential Functions

What is the inverse of an exponential function f(x) = a^x?

• f(x) = log base a of x

• f(x) = a log x

• f(x) = a^x

• f(x) = x^a

Which of the following is a property of exponential functions?

• They have a vertical asymptote.

• They decrease as x increases.

• They have a horizontal asymptote.

• Their domain is limited to positive numbers.

What is the domain of the function f(x) = log base 3 of (x - 4)?

• x > 0

• x > 4

• x < 0

• x < 4

Which function has a vertical asymptote at x = 0?

• Quadratic function

• Linear function

• Exponential function

• Logarithmic function

What is the range of a logarithmic function?

• All real numbers

• Positive numbers only

• Negative numbers only

• Non-negative numbers

Which of the following describes the growth rate of exponential functions?

• They grow quadratically.

• They grow linearly.

• They grow logarithmically.

• They grow exponentially.

How do you find the inverse of a function y = 2x + 3?

• Add 3 to both sides

• Multiply by 2

• Divide by 2

• Switch x and y, then solve for y

What is the base in the logarithmic expression y = log base 2 of (x + 3)?

• x

• 2

• 3

• x + 3

What happens to the graph of a logarithmic function when you add a constant to the argument?

• It shifts horizontally.

• It compresses horizontally.

• It stretches vertically.

• It shifts vertically.

What is the effect of a vertical shift on the graph of a logarithmic function?

• It changes the range.

• It moves the graph left or right.

• It changes the domain.

• It moves the graph up or down.