3.4 Notes Part 1 - Effects of Linear Transformations

What is the linear parent function?

• f(x) = x^2

• f(x) = x

• f(x) = |x|

• f(x) = 2x + 1

What is the slope of the linear parent function f(x) = x?

• 0

• -1

• 1

• Undefined

How does adding a positive value 'd' to f(x) (i.e., f(x) + d) affect the graph of the linear parent function?

• The graph shifts down.

• The graph shifts left.

• The graph shifts up.

• The graph shifts right.

What characteristic of a linear function is changed by translations?

• Steepness

• Direction

• Intercepts

• Shape

What type of transformation occurs when a function f(x) is changed to f(x+c)?

• Shift right

• Shift left

• Shift up

• Shift down

What type of reflection occurs when a function f(x) is transformed into -f(x)?

• Horizontal reflection across the y-axis

• Vertical reflection across the x-axis

• Horizontal reflection across the x-axis

• Vertical reflection across the y-axis

How does the graph of af(x) change when the value of a is between 0 and 1?

• The graph becomes steeper (vertical stretch).

• The graph becomes less steep (vertical compression).

• The graph shifts horizontally.

• The graph reflects across the x-axis.

What happens to the graph of f(bx) when the value of b is between 0 and 1?

• The graph becomes steeper due to horizontal compression.

• The graph becomes less steep due to horizontal stretch.

• The graph shifts vertically.

• The graph reflects across the y-axis.