Question

feature statement
x - intercept as the input powers current grows beyond 1 ampere, the motor becomes less efficient.
relative maximum or minimum at its most efficient, the motor uses about 50% of the input power.
increasing or decreasing interval the motor loses all efficiency when the current hits 3 amperes.

Explanation:

To solve this, we match each feature with its correct statement by analyzing the graph and the descriptions:

Step 1: Analyze the \( x \)-intercept

The \( x \)-intercept is where the graph crosses the \( x \)-axis (where the output is 0). The statement "The motor loses all efficiency when the current hits 3 amperes" means efficiency (output) is 0 at \( c = 3 \), so this matches the \( x \)-intercept. Wait, no—wait, let's re - check. Wait, the \( x \)-intercept is when the function value is 0. But let's check each:

• \( x \)-intercept: The \( x \)-intercept is the point where \( y = 0 \) (in terms of the graph, when the efficiency - related value is 0). The statement "The motor loses all efficiency when the current hits 3 amperes" implies that at \( c = 3 \), efficiency is 0, so this is the \( x \)-intercept. But wait, let's check the other statements.

• Relative maximum or minimum: A relative maximum or minimum is a peak or valley in the graph. The statement "At its most efficient, the motor uses about 50% of the input power" refers to a maximum (most efficient) point, so this should match "Relative maximum or minimum".

• Increasing or decreasing interval: An increasing or decreasing interval describes where the function is rising or falling. The statement "As the input power’s current grows beyond 1 ampere, the motor becomes less efficient" implies that as \( c \) (current) increases beyond 1, the efficiency (the function value) decreases, so this is about the decreasing interval, so it matches "Increasing or decreasing interval". And the statement "The motor loses all efficiency when the current hits 3 amperes" is about the \( x \)-intercept (where the function value is 0, i.e., efficiency is 0). Wait, let's correct the matching:

1. \( x \)-intercept: The motor loses all efficiency when the current hits 3 amperes (because at \( c = 3 \), the graph likely crosses the \( c \)-axis, meaning efficiency is 0).
2. Relative maximum or minimum: At its most efficient, the motor uses about 50% of the input power (a maximum efficiency point is a relative maximum).
3. Increasing or decreasing interval: As the input power’s current grows beyond 1 ampere, the motor becomes less efficient (describes the interval where the function is decreasing as \( c \) increases beyond 1).

Final Matching:

• \( x \)-intercept: The motor loses all efficiency when the current hits 3 amperes.
• Relative maximum or minimum: At its most efficient, the motor uses about 50% of the input power.
• Increasing or decreasing interval: As the input power’s current grows beyond 1 ampere, the motor becomes less efficient.

If we were to present the answer in terms of matching each feature to the statement:

Feature	Statement
Relative maximum or minimum	At its most efficient, the motor uses about 50% of the input power.
Increasing or decreasing interval	As the input power’s current grows beyond 1 ampere, the motor becomes less efficient.

If the question was to match them, the correct matches are as above.

Answer:

To solve this, we match each feature with its correct statement by analyzing the graph and the descriptions:

Step 1: Analyze the \( x \)-intercept

The \( x \)-intercept is where the graph crosses the \( x \)-axis (where the output is 0). The statement "The motor loses all efficiency when the current hits 3 amperes" means efficiency (output) is 0 at \( c = 3 \), so this matches the \( x \)-intercept. Wait, no—wait, let's re - check. Wait, the \( x \)-intercept is when the function value is 0. But let's check each:

• \( x \)-intercept: The \( x \)-intercept is the point where \( y = 0 \) (in terms of the graph, when the efficiency - related value is 0). The statement "The motor loses all efficiency when the current hits 3 amperes" implies that at \( c = 3 \), efficiency is 0, so this is the \( x \)-intercept. But wait, let's check the other statements.

• Relative maximum or minimum: A relative maximum or minimum is a peak or valley in the graph. The statement "At its most efficient, the motor uses about 50% of the input power" refers to a maximum (most efficient) point, so this should match "Relative maximum or minimum".

• Increasing or decreasing interval: An increasing or decreasing interval describes where the function is rising or falling. The statement "As the input power’s current grows beyond 1 ampere, the motor becomes less efficient" implies that as \( c \) (current) increases beyond 1, the efficiency (the function value) decreases, so this is about the decreasing interval, so it matches "Increasing or decreasing interval". And the statement "The motor loses all efficiency when the current hits 3 amperes" is about the \( x \)-intercept (where the function value is 0, i.e., efficiency is 0). Wait, let's correct the matching:

1. \( x \)-intercept: The motor loses all efficiency when the current hits 3 amperes (because at \( c = 3 \), the graph likely crosses the \( c \)-axis, meaning efficiency is 0).
2. Relative maximum or minimum: At its most efficient, the motor uses about 50% of the input power (a maximum efficiency point is a relative maximum).
3. Increasing or decreasing interval: As the input power’s current grows beyond 1 ampere, the motor becomes less efficient (describes the interval where the function is decreasing as \( c \) increases beyond 1).

Final Matching:

• \( x \)-intercept: The motor loses all efficiency when the current hits 3 amperes.
• Relative maximum or minimum: At its most efficient, the motor uses about 50% of the input power.
• Increasing or decreasing interval: As the input power’s current grows beyond 1 ampere, the motor becomes less efficient.

If we were to present the answer in terms of matching each feature to the statement:

Feature	Statement
Relative maximum or minimum	At its most efficient, the motor uses about 50% of the input power.
Increasing or decreasing interval	As the input power’s current grows beyond 1 ampere, the motor becomes less efficient.

If the question was to match them, the correct matches are as above.