Transforming Functions in Algebra

The video tutorial covers sketching functions, focusing on parabolas. It explains how adding or subtracting constants affects the vertical position of the graph, resulting in vertical shifts. The tutorial also discusses horizontal shifts by modifying the quadratic term, illustrating how these changes move the graph left or right. The explanations aim to provide a logical understanding of these transformations, rather than relying solely on memorization.

What is the shape of the graph of f(x) = x^2?

• A parabola

• A straight line

• A circle

• A hyperbola

What happens to the graph of f(x) = x^2 when it is transformed to g(x) = x^2 - 3?

• It shifts 3 units upward

• It shifts 3 units to the left

• It shifts 3 units downward

• It shifts 3 units to the right

What is the effect of subtracting a constant from the function f(x) = x^2?

• It shifts the graph horizontally

• It changes the shape of the graph

• It shifts the graph vertically

• It reflects the graph

How does the graph of h(x) = x^2 + 2 differ from the graph of f(x) = x^2?

• It shifts 2 units downward

• It shifts 2 units upward

• It shifts 2 units to the left

• It shifts 2 units to the right

What is the effect of adding a constant to the function f(x) = x^2?

• It reflects the graph

• It changes the shape of the graph

• It shifts the graph vertically

• It shifts the graph horizontally

What type of shift occurs when graphing f(x) = (x - 3)^2?

• Horizontal shift to the left

• Horizontal shift to the right

• Vertical shift downward

• Vertical shift upward

In the function f(x) = (x - 3)^2, what is the new vertex of the parabola?

• (0, 0)

• (3, 0)

• (-3, 0)

• (0, 3)

What happens to the graph of f(x) = x^2 when it is transformed to h(x) = (x + 2)^2?

• It shifts 2 units to the left

• It shifts 2 units downward

• It shifts 2 units to the right

• It shifts 2 units upward

In the function h(x) = (x + 2)^2, what is the new vertex of the parabola?

• (0, 2)

• (-2, 0)

• (2, 0)

• (0, 0)

Which of the following functions represents a horizontal shift to the left?

• f(x) = (x + 2)^2

• f(x) = x^2 - 3

• f(x) = x^2 + 2

• f(x) = (x - 3)^2