9-7 Linear, Quadratic, Exponential Models

1. The attendances at the high school basketball games seemed to be affected by the success of the team. The graph shown models the attendance over the first half of the season. Which function would also represent the data shown in the graph where a represents the attendance and g represents the number of games the team has won?

The graph shown is a decreasing linear function, which means that as the number of games won increases, the attendance decreases. This suggests that the success of the team negatively affects the attendance at the basketball games. Therefore, the function that represents this relationship is a linear function with a negative slope.

Explanation

The graph shown is a decreasing linear function, which means that as the number of games won increases, the attendance decreases. This suggests that the success of the team negatively affects the attendance at the basketball games. Therefore, the function that represents this relationship is a linear function with a negative slope.

2. Which type of function is represented by the equation

y space equals space 12 comma 575 space times space 0.88 to the power of x

?

Linear

Quadratic

Exponential

None of the above

The answer is Exponential because the question asks about the type of function represented by the equation, but the equation itself is not provided. Since there is no equation given, it is not possible to determine the specific type of function. Therefore, the correct answer is "None of the above".

Explanation

The answer is Exponential because the question asks about the type of function represented by the equation, but the equation itself is not provided. Since there is no equation given, it is not possible to determine the specific type of function. Therefore, the correct answer is "None of the above".

3. What function can be used to model data pairs that have a common ratio?

Linear

Quadratic

Exponential

None of the above

Exponential function can be used to model data pairs that have a common ratio. This is because exponential functions have a constant ratio between successive terms, which is a characteristic of data pairs that have a common ratio. Linear and quadratic functions do not have this property, so they cannot accurately model data pairs with a common ratio. Therefore, the correct answer is exponential.

Explanation

Exponential function can be used to model data pairs that have a common ratio. This is because exponential functions have a constant ratio between successive terms, which is a characteristic of data pairs that have a common ratio. Linear and quadratic functions do not have this property, so they cannot accurately model data pairs with a common ratio. Therefore, the correct answer is exponential.

4. Which kind of function best models the set of data points (1, -10), (-1, 22), (0, 6), (3, -42), (2, -26)?

Linear

Quadratic

Exponential

None of the above

A linear function best models the set of data points because the data points can be connected by a straight line. A linear function is in the form y = mx + b, where m is the slope of the line and b is the y-intercept. The given data points can be plotted on a graph and connected by a straight line, indicating that a linear function is the best fit for the data.

Explanation

A linear function best models the set of data points because the data points can be connected by a straight line. A linear function is in the form y = mx + b, where m is the slope of the line and b is the y-intercept. The given data points can be plotted on a graph and connected by a straight line, indicating that a linear function is the best fit for the data.

5. Which kind of function best models the set of data points (-3, 18), (-2, 6), (-1, 2), (0, 11), (1, 27)?

Linear

Quadratic

Exponential

None of the above

None of the above functions can accurately model the given set of data points. A linear function would result in a straight line, which does not fit the data. A quadratic function would result in a parabolic curve, which also does not fit the data. An exponential function would result in a curve that either increases or decreases rapidly, which does not match the pattern of the given data. Therefore, none of the above functions can accurately model the given data points.

Explanation

None of the above functions can accurately model the given set of data points. A linear function would result in a straight line, which does not fit the data. A quadratic function would result in a parabolic curve, which also does not fit the data. An exponential function would result in a curve that either increases or decreases rapidly, which does not match the pattern of the given data. Therefore, none of the above functions can accurately model the given data points.