Final Exam Review(Part 3)

Front

What is the distance formula used to find the distance between two points (J and K)?

Back

The distance formula is given by: d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.

Front

What does the inequality y ≤ 3x represent graphically?

Back

It represents the region below or on the line y = 3x.

Front

How do you determine the solution set of a system of inequalities?

Back

You graph each inequality and find the overlapping region that satisfies all inequalities.

Front

What is a transformation in mathematics?

Back

A transformation is an operation that moves or changes a shape in some way, such as translation, rotation, or reflection.

Front

What does it mean to translate a function left or right?

Back

Translating a function left or right involves shifting the graph horizontally along the x-axis.

Front

If f(x) = 0.5^x and g(x) = 0.5^{x-3}, what transformation occurs from g(x) to f(x)?

Back

The graph of g(x) is translated left by 3 units to obtain f(x).

Front

What is the significance of the slope in a linear inequality?

Back

The slope indicates the steepness of the line and the direction of the inequality (increasing or decreasing).

Front

How do you find the length of a side in a triangle using the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, a^2 + b^2 = c^2, where c is the hypotenuse.

Front

What is the graphical representation of y > 2x - 4?

Back

It represents the region above the line y = 2x - 4.

Front

What does the notation y < 2 mean in terms of graphing?

Back

It represents the region below the horizontal line y = 2.