Let y = f (x) be a function with domain D = [-6, 10] and range R = [-8, 12]. Find the domain D and range R for each function. Assume f (6) = 12 and f (10) = - 8. (Enter your answers using interval notation.)

a) y = - 2f (x)

b) y = |f (x) |

c) y = f (x + 2) - 3

Question

Mathematics

Alexis Eaton

4 May, 12:46

Let y = f (x) be a function with domain D = [-6, 10] and range R = [-8, 12]. Find the domain D and range R for each function. Assume f (6) = 12 and f (10) = - 8. (Enter your answers using interval notation.)

a) y = - 2f (x)

b) y = |f (x) |

c) y = f (x + 2) - 3

+1

Answers (1)

Know the Answer?

Reina Cooke · Answer 1

A) The domain remains the same.

Since, in y = - 2 f (x), the y is whats being multiplied and therefore changed, not the x or domain.

Therefore D[-6,10]

The range is what changes by a factor of - 2.

If the original range was [-8,12], then the new one is

[ (-8 x - 2), (12 x - 2) ] = [16, - 24].

However, you must flip the numbers to make the interval true, giving you R [-24,16]

Let y = f (x) be a function with domain D = [-6, 10] and range R = [-8, 12]. Find the domain D and range R for each function. Assume f (6) = 12 and f (10) = - 8. (Enter your answers using interval notation.)a) y = - 2f (x)b) y = |f (x) |c) y = f (x + 2) - 3

Let y = f (x) be a function with domain D = [-6, 10] and range R = [-8, 12]. Find the domain D and range R for each function. Assume f (6) = 12 and f (10) = - 8. (Enter your answers using interval notation.)

a) y = - 2f (x)

b) y = |f (x) |

c) y = f (x + 2) - 3