Question

1. does the table represent a function?

x | 0 | 1 | 2 | 2 | 3 | 4
f(x) | -5 | -2 | 0 | 2 | 4 | 7
a. yes b. no c. undefined d. not enough information

1. use the vertical line test to determine if the graph is a function.

image of a graph
a. yes, it is a function because it passes the vertical line test
b. no, it is not a function because it fails the vertical line test
c. yes, it is a function because it fails the vertical line test
d. no, it is not a function because it passes the vertical line test

1. the graph of a function is shown. what is the domain of the function?

image of a graph
a. $x \geq -4$ b. $x \geq -2$ c. $x \geq 0$ d. $x \geq 1$

Explanation:

Question 6

Step1: Recall function definition

A function is a relation where each input (x - value) has exactly one output (f(x) - value).

Step2: Check table values

In the table, x = 2 appears twice with different f(x) values (0 and 2). So, one input (x = 2) has multiple outputs.

Step1: Recall vertical line test

A graph represents a function if no vertical line intersects the graph more than once.

Step2: Analyze the graph

The given graph has a vertical line that intersects it more than once (from the visual), so it fails the vertical line test. Thus, it is not a function.

Step1: Recall domain definition

Domain is the set of all x - values for which the function is defined.

Step2: Analyze the graph

The graph starts at x = - 4 (the leftmost point is at x = - 4) and extends to the right, so the domain is \(x\geq - 4\).

Answer:

b. no

Question 7