Unit 3 Test Review (Review A)

Front

What is the graph of the absolute value parent function, f(x) = |x|, and what are its key characteristics?

Back

The graph of the absolute value parent function is a V-shaped graph that opens upwards. Key characteristics include: vertex at (0,0), symmetry about the y-axis, and the function is non-negative for all x.

Front

How does the transformation g(x) = 2|x - 3| + 1 affect the graph of the absolute value function?

Back

The transformation g(x) = 2|x - 3| + 1 involves a horizontal shift to the right by 3 units, a vertical stretch by a factor of 2, and a vertical shift upwards by 1 unit.

Front

What are the coordinates of the transformed key points for g(x) = 2|x - 3| + 1?

Back

The transformed key points are (0, 7), (3, 1), and (6, 7).

Front

If the point (4, -4) lies on the graph of f, what is the corresponding point on the graph of g(x) = -2f(x)?

Back

The corresponding point on the graph of g is (4, 8). This is because the transformation reflects the point across the x-axis and scales it by a factor of 2.

Front

What is an odd function, and how can you identify it graphically?

Back

An odd function is a function f(x) that satisfies f(-x) = -f(x) for all x in its domain. Graphically, it is symmetric about the origin.

Front

What is the effect of a vertical stretch on the graph of a function?

Back

A vertical stretch multiplies the output values of the function by a factor greater than 1, making the graph steeper.

Front

What is the significance of the vertex in the graph of an absolute value function?

Back

The vertex is the point where the graph changes direction. For the function f(x) = |x|, the vertex is at (0,0).

Front

How do horizontal shifts affect the graph of a function?

Back

Horizontal shifts move the graph left or right. For example, g(x) = f(x - h) shifts the graph of f to the right by h units if h > 0.

Front

What is the relationship between the transformations of a function and its key points?

Back

Transformations affect the coordinates of key points by shifting, reflecting, or stretching the graph, which can be calculated based on the transformation rules.

Front

What is the general form of an absolute value function and its transformations?

Back

The general form is f(x) = a|bx - h| + k, where a is the vertical stretch/compression, b is the horizontal stretch/compression, (h,k) is the vertex.