Final Review

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What does the notation \( (-\infty, 3) \) represent?

Back

It represents all real numbers less than 3, not including 3.

Front

What does the notation \( (3, \infty) \) represent?

Back

It represents all real numbers greater than 3, not including 3.

Front

How do you find the vertex of a parabola given its equation?

Back

The vertex can be found using the formula \( \left( -\frac{b}{2a}, f\left(-\frac{b}{2a}\right) \right) \) for a quadratic equation in the form \( ax^2 + bx + c \).

Front

What are x-intercepts of a function?

Back

X-intercepts are the points where the graph of the function crosses the x-axis, meaning the output value (y) is zero.

Front

How do you find the x-intercepts of a quadratic function?

Back

Set the quadratic equation to zero and solve for x using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) used to find the roots of a quadratic equation \( ax^2 + bx + c = 0 \).

Front

What does \( f(f^{-1}(x)) = x \) signify?

Back

This signifies that applying a function and its inverse returns the original input value x.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant \( b^2 - 4ac \) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

What is a parabola?

Back

A parabola is a symmetric curve formed by the graph of a quadratic function, characterized by its vertex and axis of symmetry.