Exploring Transformations of Functions

The video tutorial covers transformations of functions, including translations, reflections, stretches, and compressions. It explains how these transformations affect the graph of a function compared to its parent function. The tutorial also discusses combining transformations and graphing absolute value functions, providing examples and visual aids to enhance understanding.

What happens to the graph of a function if we apply a translation of f(x) = x^2 to the right by 2 units?

• Shifts right by 2 units

• Shifts up by 2 units

• No change

• Shifts left by 2 units

If a function is reflected over the x-axis, what happens to its graph?

• It flips over the y-axis

• It stretches vertically

• It flips over the x-axis

• It moves to the right

What does a negative sign outside the function notation indicate about the graph transformation?

• Reflection over the x-axis

• Reflection over the y-axis

• Vertical stretch

• Horizontal shift

What does a reflection over the y-axis do to the graph of a function?

• Shifts it right

• Shifts it left

• Flips it over the x-axis

• Flips it over the y-axis

What effect does a vertical stretch have on the graph of a function?

• Makes it wider

• Shifts it upwards

• Makes it narrower

• Shifts it downwards

If a function has a horizontal compression, how does it affect the graph?

• Shifts it right

• Shifts it left

• Makes it narrower

• Makes it wider

How does a horizontal stretch differ from a horizontal compression in terms of graph transformation?

• Both make the graph narrower

• Stretch makes the graph narrower, compression makes it wider

• Stretch makes the graph wider, compression makes it narrower

• Both make the graph wider

What transformation is indicated by a positive number inside the function's parentheses?

• Shift to the left

• Shift to the right

• Vertical stretch

• Vertical compression

Combining a vertical compression and a shift upwards, what is the expected transformation?

• Graph compresses horizontally and shifts up

• Graph compresses vertically and shifts up

• Graph stretches horizontally and shifts down

• Graph stretches vertically and shifts down

In the context of absolute value transformations, what does a negative coefficient outside the absolute value symbol indicate?

• Shift upwards

• Reflection over the x-axis

• Horizontal shift to the right

• Vertical stretch