College Algebra Test 3 Review - Autumn 2024

Front

What is the inverse of the function y = x^2 + 6x + 9?

Back

The inverse is y^{-1} = √x - 3.

Front

What is the range of the function f(x) = log_4(x - 8) + 6?

Back

The range is (-∞, ∞).

Front

What is the domain of the function f(x) = -4^{(x + 3)} - 13?

Back

The domain is (-∞, ∞).

Front

How do you simplify the logarithm log_6(3) + log_6(12)?

Back

The simplified result is 2.

Front

What are the solutions to the system of equations given in the problem?

Back

The solutions are (-8, -6) and (6, 8).

Front

What is the definition of a function's inverse?

Back

A function's inverse reverses the input and output of the original function.

Front

How do you find the inverse of a quadratic function?

Back

To find the inverse, solve for x in terms of y and then switch x and y.

Front

What is the significance of the domain in a function?

Back

The domain represents all possible input values for the function.

Front

What is the significance of the range in a function?

Back

The range represents all possible output values of the function.

Front

What is the logarithmic identity used to combine logarithms?

Back

log_b(m) + log_b(n) = log_b(m * n).