Describe how the following two functions would compare to each other.

Question

Function 1: y = 4x + 2 and Function 2: y = 4x - 1
Group of answer choices

Function 2 moved 3 units down from Function 1

Function 2 moved 2 units up from Function 1

Function 2 reflected over Function 1

Function 2 moved righ 3 units

There is no correct answer given.

Answer 1

To compare the two functions \( y = 4x + 2 \) and \( y = 4x - 1 \), we can analyze their slopes and y-intercepts.

Both functions have the same slope of 4, which means they are parallel lines. The only difference between the two functions is their y-intercepts:

• For Function 1 (\( y = 4x + 2 \)), the y-intercept is 2.
• For Function 2 (\( y = 4x - 1 \)), the y-intercept is -1.

To find the vertical distance between the two functions at their intercepts:

• The difference in the y-intercepts is \( 2 - (-1) = 3 \).

This means that Function 2 is 3 units lower than Function 1.

Thus, the correct comparison between the two functions is:

Function 2 moved 3 units down from Function 1.