
a.
To graph: The equation
a.

Answer to Problem 51PPS
Explanation of Solution
Given information:
The equation
Graph:
Figure 1.
Figure 2.
Figure 3.
Interpretation:
The linear equation
b.
To evaluate:whether each function is one-to-one and onto.
b.

Answer to Problem 51PPS
Function | One-to-One | Onto |
Yes | Yes | |
No | No | |
Yes | Yes |
Explanation of Solution
Given information:
The students spent
Formula used:
A function is a relation in which each element of the domain is paired with exactly one element in the range.
One-to −One function: Each element of the domain pairs exactly one unique element of the range.
Onto function: Each element of the range corresponds to an element of the domain.
Calculation:
According to the question,
Function | One-to-One | Onto |
Yes | Yes | |
No | No | |
Yes | Yes |
The first and last function each element in the domain is mapped to unique element of range. Whereas the second function is a constant function. This implies that every element of the domain is mapped to same number 6 of the range.
Therefore, first and last function are one-to-one and onto whereas second function is not.
c.
To proof:that all linear functions one-to-one and/or onto.
c.

Explanation of Solution
Given information:
Formula used:
Vertical−Test: If no vertical line intersects a graph in more than one point, the graph represents a function whereas if vertical line intersects a graph more than one point ,the graph does not represent a function.
Proof:
Horizontal lines are not linear. They are neither one-to-one nor onto because only one value of range is mapped with all the values present in domain.
Every other linear function is one-to-one and onto .
Therefore, each element of the domain is mapped with unique element of the range.
Chapter 2 Solutions
Algebra 2
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