6.1 Square Root Functions and Inverses

Front

What is the inverse of the function f(x) = -4x - 12?

Back

f^-1(x) = -1/4x - 3

Front

What is the result of composing a function f(x) with its inverse f^-1(x)?

Back

x

Front

What is the general form of a square root function?

Back

y = √(x - h) + k, where (h, k) is the vertex of the graph.

Front

How do you find the inverse of a function algebraically?

Back

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

Front

What is the domain of the function f(x) = √(x - 5) + 4?

Back

The domain is x ≥ 5.

Front

What is the range of the function f(x) = √(x - 5) + 4?

Back

The range is y ≥ 4.

Front

What is the effect of a negative coefficient in front of a square root function?

Back

It reflects the graph across the x-axis.

Front

What is the vertex of the function y = √(x - 5) + 4?

Back

The vertex is (5, 4).

Front

How do you determine if two functions are inverses of each other?

Back

If f(f^-1(x)) = x and f^-1(f(x)) = x for all x in the domain.

Front

What is the horizontal line test and how does it relate to inverses?

Back

A function passes the horizontal line test if no horizontal line intersects the graph more than once, indicating it has an inverse.