Transformations of Functions Intro

Front

What is a transformation of a function?

Back

A transformation of a function refers to the changes made to the graph of the function, including shifts, stretches, compressions, and reflections.

Front

What does it mean to shift a graph to the left?

Back

Shifting a graph to the left means moving every point of the graph a certain number of units in the negative x-direction.

Front

What does it mean to shift a graph to the right?

Back

Shifting a graph to the right means moving every point of the graph a certain number of units in the positive x-direction.

Front

What is the vertex form of an absolute value function?

Back

The vertex form of an absolute value function is f(x) = a|x - h| + k, where (h, k) is the vertex.

Front

What is the parent function of an absolute value function?

Back

The parent function of an absolute value function is y = |x|.

Front

How does the value of 'a' in the vertex form affect the graph?

Back

The value of 'a' affects the slope of the graph; if 'a' is positive, the graph opens upwards, and if 'a' is negative, it opens downwards.

Front

What is the effect of adding a constant 'k' to the vertex form?

Back

Adding a constant 'k' shifts the graph vertically; if k is positive, the graph shifts up, and if k is negative, it shifts down.

Front

What is the effect of subtracting a constant 'h' in the vertex form?

Back

Subtracting a constant 'h' shifts the graph horizontally; if h is positive, the graph shifts to the right, and if h is negative, it shifts to the left.

Front

What is the vertex of the function f(x) = |x - 3| + 2?

Back

The vertex of the function f(x) = |x - 3| + 2 is (3, 2).

Front

How do you determine the vertex from the function f(x) = a|x - h| + k?

Back

The vertex can be determined as the point (h, k) from the vertex form of the function.