A)
True or False
A function's graph may include solutions that do not appear in its table of values.
(1 point)
true
false
True.
A)
Multiple Choice
The total cost c a painter charges to paint a house depends on the number h of hours it takes to paint the house. This situation can be
represented by the function rule c = 15h + 245. What is the total cost if the painter works for 30.25 hours?
(1 point)
$245.00
$453.75
$572.75
$698.75
To find the total cost, we can substitute the given number of hours (30.25) into the function rule:
c = 15h + 245
c = 15(30.25) + 245
c = 453.75 + 245
c = $698.75
Therefore, the total cost if the painter works for 30.25 hours is $698.75.
To determine if the statement is true or false, we need to understand the relationship between a function's graph and its table of values.
When we have a function, we can represent it using a graph or a table of values. The graph of a function shows the relationship between its input values (x-values) and output values (y-values). The table of values, on the other hand, lists specific input-output pairs for the function.
In most cases, a function's graph and its table of values will provide the same information and include the same solutions. However, there are situations where a function's graph may include solutions that do not appear in its table of values.
One such situation is when the graph of the function has a vertical asymptote. A vertical asymptote occurs when the graph of a function gets infinitely close to a vertical line but does not actually intersect it. In this case, the x-values corresponding to the vertical asymptote will not be included in any x-values listed in the function's table of values. Therefore, the solutions corresponding to the vertical asymptote will be part of the graph but not the table of values.
Another situation is when the graph of the function has a hole or a discontinuity. A hole occurs when there is a point missing from the graph at a specific x-value. The x-value of the hole may not be represented in the table of values, but it will still be part of the function's graph.
Based on these explanations, the statement "A function's graph may include solutions that do not appear in its table of values" is true. In certain cases, the graph of a function can include solutions (such as those corresponding to vertical asymptotes or holes) that are not listed in its table of values.