Question

functions

1. which of the following does not represent a relation that is a function?

a. in a table of values, each input has exactly one output.
b. in a table of values, each input has one or more outputs.
c. the graph of the relation passes the vertical line test.
d. the equation of the relation is in the form $y = mx + b$.

1. the amount of money, $m$, in dollars, a mail carrier earns to deliver mail to h

modeled by the function $m = 3h + 200$. what input values for $h$ make sense
a. decimals b. irrational numbers
c. rational numbers d. whole numbers

1. label the graph of the relations as a function, or non - function.

(three graphs are shown here, the first graph has a curve crossing the y - axis and x - axis with a self - intersection, the second graph is a straight line passing through the origin with a negative slope, the third graph is a parabola opening upwards with vertex at the origin)

1. determine whether the mapping diagram is a function. justify your

answer.

Explanation:

Step1: Recall function definition

A function requires each input to have exactly one output.

Step2: Analyze question 1 options

• A: Meets function definition (valid).
• B: One or more outputs violates function rule (invalid).
• C: Vertical line test passes means function (valid).
• D: Linear equation \(y=mx+b\) is a function (valid).

Step3: Analyze question 2 context

\(h\) represents hours worked—must be non-negative whole numbers (decimals/rationals/irrationals don’t make sense for hours).

Step4: Apply vertical line test to graphs

• Left graph: Fails (vertical line intersects twice).
• Middle graph: Passes (straight line, no double intersections).
• Right graph: Passes (parabola, no double intersections).

Step5: Note incomplete question 4

Question 4 lacks the mapping diagram, so it can’t be answered.

Answer:

1. B. In a table of values, each input has one or more outputs.
2. D. whole numbers
3. Left graph: non-function; Middle graph: function; Right graph: function
4. Incomplete (no mapping diagram provided)