Function Transformations and Properties

The video tutorial covers the process of solving equations and understanding the difference between expressions and values. It explores graphing linear functions, analyzing their properties, and understanding function transformations such as translations and reflections. The tutorial also delves into analyzing parabolas and predicting changes in graphs using Desmos, emphasizing the importance of understanding how different transformations affect the graph's shape and position.

What is the main difference between an expression and a value?

• Both expression and value contain variables.

• Both expression and value are specific numbers.

• A value contains variables, while an expression is a specific number.

• An expression contains variables, while a value is a specific number.

What is the y-intercept of the line represented by the equation 2x - 1?

• -1

• 0

• 2

• 1

What does the gradient of a line indicate?

• The length of the line

• The x-intercept of the line

• The steepness of the line

• The y-intercept of the line

What kind of transformation is involved in finding the inverse of a function?

• Reflection

• Rotation

• Dilation

• Translation

How do you describe the movement from a red line to a blue line when translating functions?

• Dilation

• Reflection

• Translation

• Rotation

If a function is translated one unit to the left, what change is made to its equation?

• Add 1 to x

• Add 1 to y

• Subtract 1 from x

• Subtract 1 from y

What happens to a function when you change the coefficient of x to 2?

• The function becomes wider

• The function becomes steeper

• The function shifts up

• The function shifts down

What is the effect of dividing the coefficient of x by 3 in a function?

• The function becomes narrower

• The function shifts left

• The function becomes wider

• The function shifts right

In the context of function transformations, what does a positive coefficient change typically affect?

• Horizontal compression

• Vertical translation

• Horizontal translation

• Vertical compression

What is the result of adding a constant to the x variable in a function?

• Horizontal shift

• Vertical shift

• Reflection

• No change