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Please help me out with this​

Please help me out with this​-example-1
User Xanatos
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1 Answer

5 votes

Explanation:

the domain is the interval or set of all valid x- values.

the range is the interval or set of all valid y-values.

so, the domain here is (-infinity .. +infinity).

as there is clearly nothing hindering us to go all the way to the left or all the way to the right to pick an x-value for the function.

the range here is (-infinity .. +3].

as the y-value can "dive" down as deep as we want, but it cannot get larger than +3.

please consider the choice of brackets. "(", ")" means excluding the specified interval ends ("infinity" is a concept, not a value, so it can never be included).

"[", "]" means including the specified interval ends.

the function is clearly a parabola.

y = ax² + bx + c

the parabola opens downwards, so a is negative.

for x = 0, we get f(x) = 3, so c = +3

for y = 0, we get x = ±2

so,

0 = a2² + b2 + 3

and

0 = a(-2)² + b(-2) + 3

4a + 2b = -3

4a - 2b = -3

--------------------

8a 0 = -6

a = -6/8 = -3/4

4a + 2b = -3

4(-3/4) + 2b = -3

-3 + 2b = -3

2b = 0

b = 0

the function is

f(x) = (-3/4)x² + 3

User Lokesh Paunikar
by
8.1k points

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