Transformations of Linear Graphs Explained

The video tutorial covers transformations of graphs, focusing on linear functions. It explains why transformations are taught at this point in the curriculum, emphasizing their universal application across different graph types. The tutorial details translation, reflection, and stretch/compression transformations, providing examples and practice problems to reinforce understanding.

Why is it easier to see transformations on a parabola than on a straight line?

• Because straight lines do not transform.

• Because transformations are more visually obvious on parabolas.

• Because parabolas have a more complex shape.

• Because parabolas are more colorful.

What happens to a function when you add a number outside of it?

• It compresses.

• It reflects over the x-axis.

• It shifts vertically.

• It shifts horizontally.

If a change happens inside the parentheses of f(x), what does it affect?

• The y-coordinates.

• The slope.

• The origin.

• The x-coordinates.

What does a negative sign inside the function notation indicate?

• A vertical stretch.

• A horizontal stretch.

• A vertical reflection.

• A horizontal reflection.

What transformation occurs when you multiply a function by a number greater than one outside the function?

• Vertical compression.

• Horizontal stretch.

• Vertical stretch.

• Horizontal compression.

What is the reciprocal of a scale factor used for?

• Horizontal stretches.

• Vertical stretches.

• Vertical translations.

• Horizontal translations.

What transformation occurs when f(x) is replaced with f(x-2)?

• Vertical translation 2 units up.

• Horizontal translation 2 units left.

• Vertical translation 2 units down.

• Horizontal translation 2 units right.

What transformation occurs when f(x) is replaced with -f(x)?

• Horizontal reflection.

• Vertical reflection.

• Horizontal stretch.

• Vertical stretch.

What transformation occurs when f(x) is replaced with 2f(x)?

• Horizontal stretch by a factor of 2.

• Vertical stretch by a factor of 2.

• Vertical compression by a factor of 2.

• Horizontal compression by a factor of 2.

What transformation occurs when f(x) is replaced with f(x) + 3?

• Vertical translation 3 units down.

• Horizontal translation 3 units left.

• Vertical translation 3 units up.

• Horizontal translation 3 units right.