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The function h(x) is defined as shown. What is the range of h(x)?

h(x) = {
a) x + 2, x < 3
b) -x + 8, x ≥ 3
c) -5
d) Not enough information provided

User Ecodan
by
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1 Answer

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Based on the given function, the range of h(x) is f(x) ≤ 5. The correct answer is B) f(x) ≤ 5.

How to find the range

The function h(x) is defined as shown:

h(x) = x + 2, when x < 3

h(x) = -x + 8, when x ≥ 3

The question asks about the range of h(x). This means determining the set of possible output values (f(x)) for the function h(x).

For when x < 3:

As x decreases towards negative infinity, h(x) also decreases towards negative infinity.

The smallest value for this domain is h(2) = 2 + 2 = 4.

For when x ≥ 3:

As x increases towards positive infinity, h(x) decreases towards negative infinity.

The largest value for this domain is h(3) = -3 + 8 = 5.

Hence, the range of h(x) is f(x) ≤ 5 or f(x) ≥ -∞.

Among the options provided:

A) -∞ < f(x) < ∞: This represents the entire real number line, but it's not specific to the range of h(x).

B) f(x) ≤ 5: This correctly represents the range of h(x).

C) f(x) ≥ 5: This does not cover values less than 5, so it's not the complete range of h(x).

D) f(x) ≥ 3: This only covers values greater than or equal to 3, which is not the entire range of h(x).

Therefore, the correct answer among the given options is B) f(x) ≤ 5.

The function h(x) is defined as shown.

What is the range of h(x)?

A) –∞ < f(x) < ∞

B) f(x) ≤ 5

C) f(x) ≥ 5

D) f(x) ≥ 3

h(x)= { x + 2, x < 3

{ -x + 8. x ≥ 3

User Davecove
by
8.6k points

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