Question

The function h(x) is defined as shown.

Answer 1

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Answer:

  (b)  h(x) ≤ 5

Step-by-step explanation:

The maximum vertical extent of the graph is h(x) = 5 at x = 3. The range is all values of h(x) less than or equal to that:

  h(x) ≤ 5

Answer 2

Answer:  Choice B

The range is $h(x) \le 5$

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Explanation:

If we graph y = x+2, but only draw the line for x values smaller than 3, then we'll end up with the red line shown in the diagram below.

The blue line is the graph of y = -x+8, but it's only drawn when $x \ge 3$

The two lines form an upside down V shape. This is an absolute value graph.

The highest point is at the vertex (3,5). The y coordinate is y = 5. This tells us that the largest h(x) can get is h(x) = 5.

Therefore, the range is $h(x) \le 5$

This is the same as saying $y\le 5$ since y and h(x) are both outputs of a function.