2.6 Families of Functions Classwork

What is a horizontal translation of a function?

• A vertical shift of the graph up or down.

• A horizontal translation shifts the graph of a function left or right without changing its shape.

• A reflection of the graph across the x-axis.

• A change in the function's amplitude.

What is the general form of a quadratic function?

• y = ax^2 + bx + c, where a, b, and c are constants.

• y = ax^2 - bx + c, where a, b, and c are constants.

• y = a + b + c, where a, b, and c are constants.

• y = ax^2 + b, where a and b are constants.

What is a vertical stretch of a function?

• A vertical stretch increases the distance between points on the graph and the x-axis by a factor.

• A vertical stretch decreases the distance between points on the graph and the x-axis by a factor.

• A vertical stretch shifts the graph to the left or right without changing its shape.

• A vertical stretch reflects the graph across the x-axis.

How does the function y = -f(x) transform the graph of f(x)?

• It reflects the graph of f(x) over the x-axis.

• It shifts the graph of f(x) to the right.

• It stretches the graph of f(x) vertically.

• It compresses the graph of f(x) horizontally.

What is a reflection of a function over the x-axis?

• A reflection over the x-axis flips the graph of the function vertically.

• A reflection over the x-axis shifts the graph to the right.

• A reflection over the x-axis changes the function's domain.

• A reflection over the x-axis rotates the graph 90 degrees.

What does the transformation y = (x - 4)^2 represent?

• It represents a vertical translation of the parent function 4 units up.

• It represents a horizontal translation of the parent function 4 units to the right.

• It represents a reflection of the parent function across the x-axis.

• It represents a compression of the parent function by a factor of 4.

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

• It shifts the graph horizontally; positive values shift right, negative values shift left.

• It reflects the graph across the x-axis.

• Adding a constant shifts the graph vertically; positive values shift up, negative values shift down.

• It changes the slope of the graph.

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

• It shifts the graph vertically up.

• It shifts the graph vertically down.

• It stretches the graph horizontally.

• It reflects the graph across the x-axis.

How does the function y = (x + 3)^2 relate to the parent function y = x^2?

• It represents a horizontal translation of the parent function 3 units to the left.

• It represents a vertical translation of the parent function 3 units up.

• It represents a reflection of the parent function across the x-axis.

• It represents a horizontal compression of the parent function by a factor of 3.

Write the equation for a vertical translation of y = f(x) 2 units up.

• f(x) = f(x) + 2.

• f(x) = f(x) - 2.

• f(x) = f(x) + 1.

• f(x) = f(x) + 3.