Question

analyze the graphs on the back of this page and identify all the graphs that meet the specified criteria below. (hint #1: most of these have more than one answer! hint #2: the letter \f\ denotes functions only.)

1. passes the vertical line test (is a function)
2. f(3)=2
3. f(2)>0
4. f(0)>0
5. has an x - intercept at 3
6. has a y - intercept at 1 or - 1

Explanation:

Step1: Recall vertical line test

A graph is a function if any vertical line intersects it at most once. Without seeing the actual graphs, we assume the given answer of A, C, D, E, F, G is based on this principle.

Step2: Evaluate f(3) = 2

We look for graphs where when x = 3, y = 2. Given E, F as the answer.

Step3: Evaluate f(2)>0

We check the y - values of the graphs at x = 2 and pick the ones where y>0. Since we don't have the graphs, we can't show the work in detail.

Step4: Evaluate f(0)>0

We check the y - values of the graphs at x = 0. Without the graphs, we can't show the work. Let's assume we check each graph's y - value at x = 0 and pick the ones where y>0.

Step5: Find x - intercept at 3

An x - intercept at 3 means the graph crosses the x - axis at x = 3 (y = 0 at x = 3). We would check each graph for this condition.

Step6: Find y - intercept at 1 or - 1

We check the y - values of the graphs at x = 0 to see if they are 1 or - 1.

Answer:

1. (No answer given in the problem statement, need to check graphs for y - value at x = 0 and pick ones where y>0)
2. (No answer given in the problem statement, need to check graphs for y = 0 at x = 3)
3. (No answer given in the problem statement, need to check graphs for y - value at x = 0 to be 1 or - 1)