Finding Inverses and Absolute Values

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function. If the function f takes an input x to produce an output y, then the inverse function f⁻¹ takes y back to x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse of a function, replace f(x) with y, swap x and y, and then solve for y. The resulting equation is the inverse function.

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

How do you solve an equation involving absolute values?

Back

To solve an equation with absolute values, set up two separate equations: one for the positive case and one for the negative case, then solve each equation.

Front

What is the quadratic formula?

Back

Front

What does it mean to factor a quadratic equation?

Back

Front

What is the process of completing the square?

Back

Front

How do you determine the vertex of a parabola given by a quadratic equation?

Back

Front

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

Back

Front

How do you solve a quadratic equation by finding square roots?

Back

To solve a quadratic equation by finding square roots, isolate the x² term and take the square root of both sides, remembering to consider both the positive and negative roots.