Algebra II Chapter 1 Review

Front

What is the transformation rule for the function f(x) = x when g(x) = 2f(x) + 3?

Back

g(x) = 2x + 3, which means the graph is stretched vertically by a factor of 2 and translated up by 3 units.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line or plane, and there are an infinite number of points that satisfy both equations.

Front

Describe the transformation of the function f(x) = |x| when it is changed to f(x) = |x - 1|.

Back

The graph of f(x) = |x - 1| is the absolute value function translated 1 unit to the right.

Front

What is the effect of the transformation g(x) = -2f(x) - 3 on the function f(x) = x?

Back

The graph is reflected over the x-axis, stretched vertically by a factor of 2, and translated down by 3 units.

Front

What does the transformation g(x) = 3f(x) - 2 do to the function f(x) = x?

Back

The graph is stretched vertically by a factor of 3 and translated down by 2 units.

Front

What is the parent function of f(x) = |x|?

Back

The parent function is the absolute value function, which has a V shape and opens upwards.

Front

How do you identify the vertex of the function f(x) = |x - 1|?

Back

The vertex is at the point (1, 0), which is the point where the graph changes direction.

Front

What is the general form of a linear equation in two variables?

Back

The general form is Ax + By = C, where A, B, and C are constants.

Front

What does it mean for two lines to be parallel in a system of equations?

Back

It means that the lines have the same slope but different y-intercepts, resulting in no solutions.

Front

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

Back

The slope indicates the steepness of the line and the direction it is going; a positive slope rises, while a negative slope falls.