Unit 3 Test Review

Front

What is the DOMAIN of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the DOMAIN of the function f(x) = √(x + 3)?

Back

The domain is [-3, ∞) because the expression under the square root must be non-negative.

Front

Back

9

Front

What is the RANGE of a square root function?

Back

The range of a square root function is the set of all possible output values (y-values), typically starting from 0 to ∞.

Front

What is the RANGE of the function f(x) = √(x) + 1?

Back

The range is [1, ∞) because the minimum value occurs at x=0.

Front

How do you shift a radical equation right and down?

Back

To shift a radical equation right by 'h' units, replace x with (x - h). To shift down by 'k' units, subtract k from the function.

Front

Which equation shifts the function y = √(x) right 5 units and down 1 unit?

Back

y = √(x - 5) - 1.

Front

What is an inverse function?

Back

An inverse function reverses the effect of the original function, swapping the input and output.

Front

Write the inverse function of y = (2x - 1)^{1/3} + 7.

Back

y = \frac{(x - 7)^3 + 1}{2}.

Front

What is the process to find the inverse of a function?

Back

1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f^{-1}(x).