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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-

Respuesta :

sqdancefan

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, ...

... (-∞, ∞).

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