Question

8 does graph b pass the vertical line test?
9 what is the range shown in graph b?
10 what is the range shown in graph b?
11 is the left half of graph b increasing or decreasing or neither?
12 is the right half of graph b increasing or decreasing or neither?
13 what is/are the x-intercepts of graph b?
14 what is/are the y-intercept of graph b?
table c
15 does table c represent a function?
16 what is the range shown in graph b?

Explanation:

Step1: Vertical Line Test

A graph passes the vertical line test if any vertical line drawn intersects the graph at most once. For Graph B, any vertical line will intersect it at most once. So, it passes the vertical line test.

Step2: Domain

The domain is the set of all \(x -\)values. Looking at the graph, the left - most \(x -\)value is \(- 2\) and the right - most \(x -\)value is \(6\). So, the domain is \(\{-2\leq x\leq6\}\).

Step3: Range

The range is the set of all \(y -\)values. The lowest \(y -\)value is \(0\) (at the endpoints) and the highest \(y -\)value is \(9\) (at the vertex). So, the range is \(\{0\leq y\leq9\}\).

Step4: Left - half behavior

For the left - half of the graph (from \(x=-2\) to \(x = 2\)), as \(x\) increases, \(y\) increases. So, it is increasing.

Step5: Right - half behavior

For the right - half of the graph (from \(x = 2\) to \(x=6\)), as \(x\) increases, \(y\) decreases. So, it is decreasing.

Step6: \(x -\)intercepts

The \(x -\)intercepts are the points where \(y = 0\). From the graph, the \(x -\)intercepts are \(x=-2\) and \(x = 6\).

Step7: \(y -\)intercept

The \(y -\)intercept is the point where \(x = 0\). From the graph, when \(x = 0\), \(y=8\). So, the \(y -\)intercept is \(y = 8\).

Step8: Function in Table C

A function is a relation where each input (\(x\)) has exactly one output (\(y\)). In Table C, for each \(x\) value (\(1,2,3,4,5\)), there is exactly one \(y\) value (\(6,10,13,15,16\)). So, it represents a function.

Step9: Linear or non - linear in Table C

For a linear function, the rate of change \(\frac{\Delta y}{\Delta x}\) is constant. \(\frac{10 - 6}{2 - 1}=4\), \(\frac{13 - 10}{3 - 2}=3\). Since the rate of change is not constant, it is a non - linear function.

Answer:

1. Yes.
2. \(\{-2\leq x\leq6\}\).
3. \(\{0\leq y\leq9\}\).
4. Increasing.
5. Decreasing.
6. \(x=-2\) and \(x = 6\).
7. \(y = 8\).
8. Yes.
9. Non - linear.