Transformations of Functions: Vertical and Horizontal Changes

The video tutorial covers transformation rules for functions, focusing on stretching, shrinking, and shifting. It explains the effects of coefficients and constants on parent functions, using examples to illustrate reflections and translations. The importance of the order of transformations is emphasized, and techniques for factoring negatives and translating lines are discussed. Basic graphing techniques for quadratics and absolute values are also demonstrated.

What happens to a parabola when a coefficient greater than 1 is placed in front of the function?

• It shifts to the right.

• It shifts to the left.

• It becomes narrower.

• It becomes wider.

If h is positive in the equation, which direction does the graph shift?

• Down

• Up

• Right

• Left

What is the effect of adding a number to the end of a function?

• Reflects the graph across the x-axis

• Reflects the graph across the y-axis

• Shifts the graph up or down

• Shifts the graph left or right

What transformation occurs when a negative sign is placed in front of the function?

• Reflection across the y-axis

• Reflection across the x-axis

• Vertical shrink

• Vertical stretch

In the equation x + 2, what does the +2 indicate?

• Shift 2 units to the right

• Shift 2 units to the left

• Shift 2 units down

• Shift 2 units up

Why is the order of transformations important?

• It does not matter.

• It affects the final shape of the graph.

• It only matters for vertical shifts.

• It only matters for horizontal shifts.

What should you do when there is a negative in front of the x in an absolute value function?

• Factor out the negative

• Ignore the negative

• Subtract a positive number

• Add a positive number

How do you reflect a function across the y-axis?

• Make the entire function negative

• Make the x negative

• Add a positive number

• Subtract a positive number

What is the parent function of a quadratic equation?

• y = 1/x

• y = x^2

• y = x

• y = |x|

How do you graph the parent function of y = x^2?

• Plot points where x equals y

• Plot points where y equals x squared

• Plot points where y equals the absolute value of x

• Plot points where y equals 1/x