Algebra III Semester 1 Review Ch 1-4

Front

Describe the transformations from the original parent function f(x) = x² to g(x) = ⅔(x - 7)².

Back

Vertical compression of ⅔ and a right shift of 7.

Front

What is the value of the determinant for the matrix?

Back

-24

Front

Multiply and simplify: (n - 10)(n + 7) / 8n + 56.

Back

(n - 10) / 8.

Front

When dividing x⁶ + 4x³ + 2 using synthetic division, how many 0's are needed in the top row?

Back

4.

Front

Identify the point that is a relative maximum: (1, 4), (0, 2), (-1, 0), (2, 0).

Back

(1, 4).

Front

What is the parent function of a quadratic equation?

Back

f(x) = x².

Front

Define vertical compression in the context of transformations.

Back

A vertical compression occurs when the output values of a function are multiplied by a factor less than 1.

Front

What does it mean to shift a function to the right?

Back

To shift a function to the right means to add a positive value to the x-variable in the function's equation.

Front

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

Back

For a matrix [[a, b], [c, d]], the determinant is ad - bc.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor.