Answer:
3. continuous; 0 ≤ x ≤ 12; 0 ≤ y ≤ 6
4. discrete; domain: {2, 4, 6, 8}; range: {10, 18, 26, 34}
Step-by-step explanation:
You don't need to "try everything." You only need to learn the vocabulary.
<h3>3.</h3>
A) A <em>continuous</em> function is one whose graph can be drawn <em>without lifting your pencil</em>. The graph shown is one continuous downward sloping line between the two marked points (0, 6) and (12, 0). The function is continuous.
B) The <em>domain</em> of a function is the <em>horizontal extent</em> of its graph, the <em>set of input values</em> for which output values are defined. This graph extends from x=0 to x=12, so the domain is ...
0 ≤ x ≤ 12
C) The <em>range</em> of a function is the <em>vertical extent</em> of its graph, the <em>set of output values</em> it produces. This graph extends from y=0 to y=6, so the range is ...
0 ≤ y ≤ 6
<h3>4.</h3>
A) The problem statement tells you the domain is a particular set of positive numbers. If you were to graph it, you would have to lift your pencil between plots of the <em>specific points</em> listed. The function is discrete.
B) The problem statement tells you the domain is a particular set of numbers. It is probably easiest to simply list them:
{2, 4, 6, 8} . . . . . . . . domain; positive even numbers less than 10
C) The expression for y tells you how to find the output values associated with these input values. The list of output values is the range of the function.
y = 4x +2 = 4(2, 4, 6, 8} +2 = (8, 16, 24, 32} +2 = {10, 18, 26, 34}
The range is ...
{10, 18, 26, 34} . . . . . the set of output values from the function
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<em>Additional comment</em>
The graph of the function in problem 4 would be the four specific points (2,10), (4,18), (6,26), (8,34). That's it, the whole graph.
