Front

What is the exponential form of the logarithmic equation \(\log_3 9 = 2\)?

Back

The exponential form is \(3^2 = 9\).

Front

How does the function \(y = |x|\) transform to \(y = |x - 4|\)?

Back

The transformation is a shift to the right by 4 units.

Front

If a culture of bacteria starts with 5000 cells and dies by 30% each year, what is the equation representing this situation?

Back

The equation is \(y = 5000(0.7)^x\).

Front

What is the inverse of the function \(f(x) = 2x - 2\)?

Back

The inverse is \(f^{-1}(x) = \frac{1}{2}x + 1\).

Front

Solve the equation: \(2(4^{3x - 6}) - 8 = 120\)

Back

The solution is \(x = 3\).

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number.

Front

What is the parent function of an absolute value function?

Back

The parent function is \(y = |x|\).

Front

What does the base of a logarithm represent?

Back

The base of a logarithm represents the number that is raised to a power.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, swap the x and y variables and solve for y.

Front

What is the general form of an exponential decay function?

Back

The general form is \(y = a(1 - r)^t\), where \(a\) is the initial amount, \(r\) is the decay rate, and \(t\) is time.