Fall 24 Algebraic Reasoning Final Exam Review Part 4

Front

What is a system of linear inequalities?

Back

A system of linear inequalities consists of two or more inequalities that share the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does the graph of y ≤ 2x - 1 represent?

Back

The graph represents all points (x, y) where y is less than or equal to the line y = 2x - 1, including the line itself.

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 for a function to have a range of all real numbers greater than or equal to -6?

Back

It means that the lowest value the function can output is -6, and it can produce any value above -6.

Front

What is a vertical translation of a graph?

Back

A vertical translation moves the graph up or down without changing its shape. For example, moving a graph 2 units up means adding 2 to the y-values.

Front

What is a horizontal translation of a graph?

Back

A horizontal translation shifts the graph left or right. For example, moving a graph 2 units left means subtracting 2 from the x-values.

Front

What is a reflection of a graph?

Back

A reflection flips the graph over a specific axis. For example, reflecting over the x-axis changes the sign of the y-values.

Front

What is a vertical stretch of a graph?

Back

A vertical stretch increases the distance between points on the graph and the x-axis, making the graph taller. For example, multiplying the function by a factor greater than 1 stretches it.

Front

How do you find the solution to a system of equations graphically?

Back

The solution is found at the point where the graphs of the equations intersect.