Transformations of Linear Functions Explained

What does a translation of a linear function primarily affect?

• The curvature of the function

• The x-intercept of the function

• The y-intercept of the function

• The slope of the function

If a linear function is translated 3 units up, what happens to its graph?

• It becomes steeper

• It becomes flatter

• It moves 3 units up

• It moves 3 units to the right

How does adding a positive constant to the y-intercept of a linear function affect its graph?

• Shifts it up

• Shifts it left

• Shifts it right

• Shifts it down

What defines a vertical dilation of a linear function?

• Multiplying both the slope and y-intercept by a constant

• Reflecting the function across the x-axis

• Multiplying the x-coordinate by a constant

• Adding a constant to the y-intercept

A horizontal compression of a linear function occurs when the multiplier is:

• Less than 1

• Greater than 1

• Equal to 0

• Equal to 1

What happens to a linear function when it undergoes a vertical stretch?

• It reflects across the y-axis

• It moves horizontally

• It becomes flatter

• It becomes steeper

In a horizontal dilation, what aspect of the linear function is directly modified?

• The slope

• The y-intercept

• The curvature

• The x-intercept

What is the effect of a horizontal stretch on a linear function's graph?

• Makes it steeper

• Makes it flatter

• Makes it wider

• Makes it narrower

What is the result of reflecting a linear function across the y-axis?

• The x-intercept becomes negative

• The y-intercept becomes negative

• The function becomes steeper

• The slope becomes negative

Combining a reflection with a vertical dilation, what changes occur to the function?

• The function flips and becomes flatter

• The x-intercept becomes the new y-intercept

• The function flips and becomes steeper

• The slope and y-intercept remain unchanged