Question

The Function h(x) is defined as shown. What is the range of h(x)?
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Answer 1

Answer:

$h(x)\leq 5$

Step-by-step explanation:

Piecewise Function

The given function has a point where its behavior changes. At the left side of x=3 the function is

$h(x)=x+2$

While at the right side the function is

$h(x)=-x+8$

We need to find the range of h, i.e. the values h takes when x moves along its domain. Let's analyze what values takes h when x decreases without limit.

$\lim\limits_{x \rightarrow -\infty }(x+2)=-\infty$

When x=3

$h(3)=-3+8=5$

When x increses without limit

$\lim\limits_{x \rightarrow \infty }(-x+8)=-\infty$

As shown, the values of h run from $-\infty$ to 5, i.e.

$Range \ h=(-\infty , 5]$

Or, equivalently

$\boxed{h(x)\leq 5}$

Answer 2

Answer:

h(x) ≤ 5 is the corrects answer

Step-by-step explanation:

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