Algebra Semester Review

Front

What is an absolute value function?

Back

An absolute value function is a function that outputs the non-negative value of its input. The parent function is represented as f(x) = |x|.

Front

What does the transformation g(x) = |3x - 4| + 5 represent?

Back

This function represents a horizontal shift to the right by 4/3 units and a vertical shift upwards by 5 units from the parent function f(x) = |x|.

Front

How do you express the domain of the function f(x) = \frac{(x+6)}{3} in interval notation?

Back

The domain is (-∞, ∞) because there are no restrictions on the values of x.

Front

What is the range of the function f(x) = \frac{(x+6)}{3}?

Back

The range is also (-∞, ∞) because the function can take any real number value.

Front

What is a matrix representation of a system of equations?

Back

A matrix representation organizes the coefficients of the variables in a rectangular array. For example, the system represented by [5, 4, -1, 1], [2, -2, 1, 1], [-1, -1, 1, 2] corresponds to a system of equations.

Front

What does it mean if an equation has a maximum value?

Back

An equation has a maximum value if the highest point of its graph is at that value, indicating that the function does not exceed this value.

Front

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

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

How do you solve the equation |2x + 3| = 5?

Back

To solve |2x + 3| = 5, set up two equations: 2x + 3 = 5 and 2x + 3 = -5. Solving these gives x = 1 and x = -4.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the term 'vertical transformation' refer to in functions?

Back

A vertical transformation refers to shifting the graph of a function up or down, typically represented by adding or subtracting a constant from the function.