The graph of f (x) = 18x is reflected about the x-axis and shifted upward 8 units. What is the equation of the new function, g (x) ?

g (x) =

State the y-intercept of g (x).

(x, y) =

State the domain and range of g (x). (Enter your answers using interval notation.)

domain-

range-

Answer: g (x) = - 18x + 8 y-intercept: (0, 8) domain: (-∞, ∞) range: (-∞, ∞) Explanation:

Reflecting a function across the x-axis changes every y-value to its opposite. That is, f (x) = 18x becomes g (x) = - 18x.

Shifting a function upward 8 units adds 8 to every y-value. That is, g (x) becomes g (x) + 8.

The combined effect of these two transformations on f (x) is to give you ...

... g (x) = - 18x + 8

You recognize this as the equation of a line in slope-intercept form, with the y-intercept being + 8. That is, g (0) = - 18·0 + 8 = 8. The y-intercept is ...

... (0, 8)

The domain and range of any linear equation is "all real numbers," that is, ...

... (-∞, ∞).