Pythagorean Theorem, Functions, Translations

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

Front

How do you find the length of a missing side in a right triangle using the Pythagorean Theorem?

Back

To find the length of a missing side, rearrange the Pythagorean Theorem formula. If you know the lengths of two sides, you can solve for the third side.

Front

If one side of a right triangle is 12 and the other is 36, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 12² + 36²; c² = 144 + 1296; c² = 1440; c = √1440 ≈ 37.95.

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as f(x), where x is the input.

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 is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean to translate a function?

Back

Translating a function means shifting its graph horizontally, vertically, or both, without changing its shape.

Front

If the function f(x) = x² is translated 3 units to the right, what is the new function?

Back

The new function is f(x) = (x - 3)².

Front

What are the coordinates of a point after a 90-degree clockwise rotation around the origin?

Back

For a point (x, y), after a 90-degree clockwise rotation, the new coordinates will be (y, -x).

Front

If the coordinates of point R are (3, 4), what are the coordinates after a 90-degree clockwise rotation?

Back

The new coordinates of point R after a 90-degree clockwise rotation will be (4, -3).