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Why are the graph(s) not a function?

Which graph(s) are NOT a function?
Which graph(s) are not linear?
Which graph(s) have a constant rate of change?

One is a circle
one is decreasing from (0, 1) going down through x
one is spiking up from (-2, 3) then going does through (0, 0) going up again through (2, 0)

Answers:
Graph a
Graph b
Graph C
Graph a and C
Graph b and C
Graph a and B
Because each input does not have exactly one output
Because each output does not have exactly one input
Because it is not linear
Because the graph increases and decreases

3 answers

Based on your descriptions of the graphs, let's analyze each one to answer your questions:

  1. Which graph(s) are NOT a function?

    • Graph a (circle): This graph is not a function because it fails the vertical line test; a vertical line can intersect the circle at two points, meaning a single input (x-value) has multiple outputs (y-values).
    • Graph b (decreasing line): This graph is a function because each x-value has exactly one y-value.
    • Graph c (spiking and changing direction): This graph behaves similarly in that it intersects the vertical line in multiple places as it spikes and drops, but without further detail, it's unclear if it has repeated outputs for the same x. However, if it does return to previous y-values, it can also fail the function definition.

    So, for clarity, Graph a is confirmed not to be a function.

  2. Which graph(s) are not linear?

    • Graph a (circle): This is not a linear graph.
    • Graph b (decreasing line): This is a linear graph.
    • Graph c (spiking graph): This likely is not linear, as it has a change in direction and is not a straight line.

    Thus, Graph a and Graph c are not linear.

  3. Which graph(s) have a constant rate of change?

    • Graph a (circle): This does not have a constant rate of change.
    • Graph b (decreasing line): This has a constant rate of change as it is a straight line with a consistent slope.
    • Graph c (spiking graph): This does not have a constant rate of change due to its non-linear behavior.

    Therefore, only Graph b has a constant rate of change.

Summary of Answers:

  • Which graph(s) are NOT a function?: Graph a (and possibly Graph c depending on specifics)
  • Which graph(s) are not linear?: Graph a and Graph c
  • Which graph(s) have a constant rate of change?: Graph b

Additional Clarifications:

  • Each input must have exactly one output for a graph to be considered a function.
  • Each output can have one or more inputs for it to not violate function principles; it's the input's multiple outputs that violate function rules.
  • The linearity is characterized by constant rates of change (straight lines vs curves).

If you have specific graph images or further details about these graphs, please share them for more accurate analysis.

Which answer answers the question:

Why are the graph(s) not a function?

The correct answer to the question "Why are the graph(s) not a function?" is:

Because each input does not have exactly one output.

This statement directly addresses the definition of a function, which requires that for every input (x-value), there is exactly one corresponding output (y-value). If a graph fails to meet this criterion, it cannot be classified as a function.