Exploring Vertical Translations of Linear Equations

What is the basic linear function that serves as the parent for all linear transformations?

• F(x) = x - 1

• F(x) = x

• F(x) = x + 1

• F(x) = 2x

In function notation, what does F(-2) = 3 specifically tell us?

• The input is 2 and the output is -3

• The input is 3 and the output is 2

• The input is 3 and the output is -2

• The input is -2 and the output is 3

What is the main difference between the graphs of F(x) and G(x) in terms of their Y-intercepts?

• F(x) has a Y-intercept of 1, G(x) has a Y-intercept of 4

• F(x) has a Y-intercept of 0, G(x) has a Y-intercept of 3

• Both have the same Y-intercept

• F(x) has a Y-intercept of 3, G(x) has a Y-intercept of 0

How does the slope of F(x) compare to the slope of G(x)?

• The slopes are negative

• Both have the same slope

• G(x) has a greater slope than F(x)

• F(x) has a greater slope than G(x)

What is the algebraic representation of G(x) if F(x) = x and G(x) is vertically translated by 3 units?

• G(x) = x + 1

• G(x) = x

• G(x) = x + 3

• G(x) = x - 3

If F(x) = x + 3 and G(x) = x + 7, what is the vertical translation from F(x) to G(x)?

• Translation of +7

• Translation of +5

• Translation of +4

• Translation of +3

How do we express a vertical translation of +4 in coordinate notation?

• (x, y) -> (x, y + 4)

• (x, y) -> (x + 4, y)

• (x, y) -> (x, y - 4)

• (x, y) -> (x - 4, y)