Shifting Functions

Front

What is a transformation in the context of functions?

Back

A transformation refers to the change in position, size, or shape of a graph of a function. Common transformations include translations, reflections, stretches, and compressions.

Front

What does it mean to translate a function to the left?

Back

Translating a function to the left means shifting the graph horizontally in the negative x-direction. For example, y = f(x + c) translates the graph of f(x) left by c units.

Front

What does it mean to translate a function down?

Back

Translating a function down means shifting the graph vertically in the negative y-direction. For example, y = f(x) - c translates the graph of f(x) down by c units.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How does the value of 'a' in a quadratic function affect its graph?

Back

The value of 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens. It can be found using the formula (-b/2a, f(-b/2a)).

Front

What does the notation |x| represent?

Back

The notation |x| represents the absolute value of x, which is the distance of x from 0 on the number line, always non-negative.

Front

What is the effect of adding a constant to a function?

Back

Adding a constant to a function translates the graph vertically. For example, y = f(x) + c shifts the graph up by c units.

Front

What is the effect of subtracting a constant from a function?

Back

Subtracting a constant from a function translates the graph vertically down. For example, y = f(x) - c shifts the graph down by c units.

Front

How do you identify the transformation of the function y = |x + 2| - 1?

Back

This function is translated left 2 units and down 1 unit from the parent function y = |x|.