Graphing Functions and Solving Equations

Flashcards covering key concepts from the lecture notes on graphing functions, finding domains and ranges, and solving equations.

What is the domain of the function f(x) = √x - 1 + 3?

The domain is x ≥ 0.

What is the range of the function f(x) = √x - 1 + 3?

The range is y ≤ 3.

How do you find the inverse of the function f(x) = -√x + 3?

Set x = -√y + 3 and solve for y.

What are the three transformations you can make on the function f(x) = -√x + 3?

Stretch/compress, reflection, and shifts.

What is the rational equation associated with f(x) = √√x + 2 - 1?

The equation can be set as y + 1 = √√x + 2.

What is the solution for the equation x² - 2x - 3 = 0?

x = 3 or x = -1.

What is the result of simplifying (2x + 5) - 1 = (x + 2)²?

You obtain the equation x² + 4x + 4 = 4x + 8.

What happens to the expression 2dx when simplified in terms of radicals?

It can be simplified to √(2x + 5) = (x + 2) + 1.