What’s the answer (question to much to type).

If the function f (x) has a domain of (a,b] and a range of [c,d), then what is the domain and range of g (x) = m × f (x) + n?

xz_007 [3.2K]

<h3>Answer: Choice A</h3>

Domain = (a,b]

Range = [mc + n,md + n)

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Explanation:

The domain stays the same because we still have to go through f(x) as our first hurdle in order to get g(x).

Think of it like having 2 doors. The first door is f(x) and the second is g(x). The fact g(x) is dependent on f(x) means that whatever input restrictions are on f, also apply on g as well. So going back to the "2 doors" example, we could have a problem like trying to move a piece of furniture through them and we'd have to be concerned about the f(x) door.

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The range will be different however. The smallest value in the range of f(x) is y = c as it is the left endpoint. So the smallest f(x) can be is c. This means the smallest g(x) can be is...

g(x) = m*f(x) + n

g(x) = m*c + n

All we're doing is replacing f with c.

So that means mc+n is the starting point of the range for g(x).

The ending point of the range is md+n for similar reasons. Instead of 'c', we're dealing with 'd' this time. The curved parenthesis says we don't actually include this value in the range. A square bracket means include that value.

6 0

2 years ago

Solve the system of equations. y=23x–19 x2–y= – 6x–23 Write the coordinates as integers, simplified proper or improper fractions

forsale [732]

Answer:

(3, 50) and (14,303)

Step-by-step explanation:

Given the system of equations;

y=23x–19 ....1

x²–y= – 6x–23 ...2

Substitute 1 into 2;

x²–(23x-19)= – 6x–23