High School

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Question 1 (Multiple Choice)

Which statement best explains whether the following table represents a linear or nonlinear function?

\[
\begin{array}{cc}
x & -2 & -1 & 0 & 1 & 2 \\
y & 4 & 2 & 0 & 2 & 4 \\
\end{array}
\]

A. The table represents a nonlinear function because there is not a constant rate of change in the input values.
B. The table represents a nonlinear function because there is not a constant rate of change in the output values.
C. The table represents a linear function because there is a constant rate of change in the input and output values.
D. The table represents a linear function because there is not a constant rate of change in the input and output values.

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Question 2 (Multiple Choice)

Which statement best explains whether the following graph represents a linear or nonlinear function?

Coordinate plane with a graph drawn that passes through the points (-1, 0), (0, -2), and (1, -4).

A. The graph represents a nonlinear function because there is a constant rate of change.
B. The graph represents a nonlinear function because the rate of change is not constant.
C. The graph represents a linear function because there is a constant rate of change.
D. The graph represents a linear function because the rate of change is not constant.

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Question 3 (Multiple Choice)

Which of the following equations represents a linear function?

A. \(2x - 4 = 6\)
B. \(x = -2\)
C. \(y = \frac{1}{2} x^2\)
D. \(y = \frac{2}{3} x + 4\)

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Question 4 (Multiple Choice)

Which of the following tables represents a linear function?

\[
\begin{array}{cc}
x & -2 & -1 & 0 & 1 & 2 \\
y & 5 & 2 & 1 & 2 & 5 \\
\end{array}
\]

\[
\begin{array}{cc}
x & -2 & -1 & 0 & 1 & 2 \\
y & 5 & 3 & 1 & -1 & -3 \\
\end{array}
\]

\[
\begin{array}{cc}
x & 3 & 3 & 0 & 3 & 3 \\
y & -2 & -1 & 0 & 1 & 2 \\
\end{array}
\]

\[
\begin{array}{cc}
x & 0 & 1 & 2 & 3 & 4 \\
y & 0 & -1 & 2 & -3 & 4 \\
\end{array}
\]

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Question 5 (Multiple Choice)

Which of the following graphs represents a linear function?

Coordinate plane with a graph that passes through the points (-2, 0), (0, -2), (2, 0), and (0, 2).

Coordinate plane with a graph drawn that passes through the points (-1, -2), (-1, -1), and (-1, 0).

Coordinate plane with a graph drawn that passes through the points (-1, 4), (0, 1), and (1, -2).

Coordinate plane with a graph that passes through the points (-3, 0), (-1, 4), (1, 4), and (3, 0).

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Question 6 (Multiple Choice)

Which statement best explains whether the equation \(y = 2x - 4\) represents a linear or nonlinear function?

A. The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.
B. The equation represents a linear function because its graph contains the points (0, 2), (2, 3), and (4, 4), which are on a straight line.
C. The equation represents a nonlinear function because it has an independent and a dependent variable, each with an exponent of 1.
D. The equation represents a nonlinear function because its graph contains the points (0, 2), (2, 3), and (4, 4), which are not on a straight line.

---

Question 7 (Multiple Choice)

Which statement best explains whether the data in the following table represents a linear or nonlinear function?

\[
\begin{array}{cc}
x & y \\
-4 & 4 \\
-1 & 2.5 \\
0 & 2 \\
4 & 0 \\
\end{array}
\]

A. The table represents a nonlinear function because the graph shows a rate of change that is decreasing.
B. The table represents a linear function because the graph shows a rate of change that is increasing.
C. The table represents a nonlinear function because the graph does not show a constant rate of change.
D. The table represents a linear function because the graph shows a constant rate of change.

Answer :

Answer:

  1. The table represents a nonlinear function because there is not a constant rate of change in the output values.
  2. The graph represents a nonlinear function because the rate of change is not constant.
  3. y equals two thirds times x plus 4 .
  4. x −2 −1 0 1 2, y 5 2 1 2 5
  5. coordinate plane with a graph that passes through the points negative 2 comma 0 and 0 comma negative 2 and 2 comma 0 and 0 comma 2
  6. The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.
  7. The table represents a nonlinear function because the graph does not show a constant rate of change.

Explanation:

Question 1 asks whether a given table represents a linear or nonlinear function. To determine this, one needs to check whether there is a constant rate of change between input (x) and output (y) values. In this case, the table represents a nonlinear function because the rate of change is not constant. The y values increase from 4 to 2 to 0 and then increase again, indicating a U-shaped curve.

Question 2 asks the same question but with a graph provided. In this case, the graph represents a nonlinear function because the rate of change is not constant. The points do not form a straight line but instead create a curved shape.

Question 3 asks which of the given equations represents a linear function. Only one of the equations, y equals two thirds times x plus 4, follows the general form y = mx + b, and thus represents a linear function.

Question 4 asks which of the given tables represents a linear function. The first and fourth tables have a constant rate of change, as the y values increase by the same amount for each increase in x, and thus represent linear functions.

Question 5 asks which of the given graphs represents a linear function. The first graph represents a linear function because the points form a straight line. The other graphs do not form straight lines, indicating nonlinear functions.

Question 6 asks whether a given equation represents a linear or nonlinear function. The equation represents a linear function because it follows the general form y = mx + b and its graph produces a straight line.

Question 7 asks whether a given table represents a linear or nonlinear function. The table represents a nonlinear function because the graph does not show a constant rate of change. The rate of change appears to be decreasing, as the y values decrease more rapidly for larger x values.

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