Transformations of Functions: Day 1 Insights

Miss Pierce explains transformations of functions, including vertical and horizontal shifts, and reflections across axes. She demonstrates how to shift graphs up, down, left, and right, and how to reflect them over the x and y axes. The video includes examples and explanations of function notation and the effects of transformations on graph coordinates.

What happens to the graph of a function when a positive value is added to it?

• It shifts downwards.

• It shifts to the right.

• It shifts to the left.

• It shifts upwards.

If a function f(x) is transformed to g(x) = f(x) - 5, what is the effect on the graph?

• It shifts 5 units right.

• It shifts 5 units up.

• It shifts 5 units down.

• It shifts 5 units left.

What is the transformation rule for shifting a function B(x) up by 4 units?

• R(x) = B(x - 4)

• R(x) = B(x) - 4

• R(x) = B(x + 4)

• R(x) = B(x) + 4

How do you horizontally shift a graph to the left by H units?

• Add H to the function.

• Subtract H from the function.

• Add H inside the parentheses with x.

• Subtract H inside the parentheses with x.

What is the effect of the transformation f(x - 7) on the graph of f(x)?

• It shifts 7 units left.

• It shifts 7 units down.

• It shifts 7 units right.

• It shifts 7 units up.

If f(x) = x and g(x) = x + 3, what is the x-value when g(x) = 0?

• 0

• 1

• -3

• 3

What happens to the y-values of a function when it is reflected across the x-axis?

• They remain the same.

• They are doubled.

• They are halved.

• They are negated.

If k(x) = -f(x), what is the transformation applied to f(x)?

• Vertical shift down.

• Vertical shift up.

• Reflection across the y-axis.

• Reflection across the x-axis.

When a function is reflected across the y-axis, what happens to the x-values?

• They are doubled.

• They are halved.

• They are negated.

• They remain the same.

What is the effect on the graph of f(x) when it is transformed to p(x) = f(-x)?

• It shifts to the left.

• It reflects across the y-axis.

• It shifts to the right.

• It reflects across the x-axis.