Chapter 5 Wrap Up

Front

What is the effect of shifting a radical equation to the right by 5 units and down by 1 unit?

Back

The equation will take the form y = √(x - 5) - 1.

Front

What is the condition for a matrix to have an inverse?

Back

A matrix has an inverse if it is square and its determinant is non-zero.

Front

How can you determine if two matrices are inverses of each other?

Back

Two matrices A and B are inverses if A * B = I, where I is the identity matrix.

Front

What is the general form of a radical function?

Back

A radical function can be expressed as f(x) = √(x - h) + k, where (h, k) is the vertex.

Front

What does it mean if a matrix has no inverse?

Back

It means the matrix is singular, typically because its determinant is zero.

Front

How do you find the inverse of a 2x2 matrix?

Back

For a matrix A = [[a, b], [c, d]], the inverse is A^(-1) = (1/det(A)) * [[d, -b], [-c, a]], where det(A) = ad - bc.

Front

What is the significance of the vertex in a radical function?

Back

The vertex represents the minimum or maximum point of the graph, depending on the direction of the opening.

Front

What is the relationship between the determinant and the invertibility of a matrix?

Back

If the determinant of a matrix is zero, the matrix is not invertible (singular). If it is non-zero, the matrix is invertible.

Front

How do transformations affect the graph of a function?

Back

Transformations such as shifts, stretches, and reflections change the position and shape of the graph.

Front

What is the graphical representation of the function f(x) = √(x - 4) - 2?

Back

This function represents a radical graph shifted right 4 units and down 2 units.