Refine: Analyzing Functional Relationships Qualitatively

Is the function increasing or decreasing from 2 < x < 6?

• Increasing

• Decreasing

Is the function decreasing at a constant or varying rate from 2 < x < 6?

• Constant

• Varying

Write the correct word in each blank to describe the function at the right.

When  4 < x < 6, the function _____ is at a _____ rate.

• increasing; constant

• increasing; varying

• decreasing; constant

• decreasing; varying

What information about a function is NOT provided by a qualitative description?

• The direction of the graph in each interval or section

• The rate of change for each linear section of the graph

• The shape of the graph (linear or nonlinear)

• Whether the function is changing at a constant rate

Akiko is painting a room in her house. The graph shows the area Akiko has painted as a function of time. Which description is correct?

• For the first 2 hours, Akiko paints very quickly at first, but then slows down.

• For 2 < x < 3, Akiko paints at a constant rate.

• For 3 < x < 4, Akiko continues painting at the same rate.

• For the last 2 hours, Akiko paints at a constant rate, but much more slowly than earlier in the day.

Arrange the qualitative description of the function.

I. The function increases at a constant rate.

II. The function increases at a varying rate.

III. The function decrease at a constant rate.

IV. The function decrease at a varying rate.

• I, II, III

• I, II, IV

• II, I, III

• II, I, IV

Jesse walks to the bus stop, waits for the bus, and then takes the bus to school. Which of the following graphs represent parts of Jesse’s trip to or from school? Assume both Jesse and the bus are moving at constant rates.

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Jesse waits for his father to pick him up after school, and his father drives him home. Which of the following graphs represent parts of Jesse’s trip to or from school? Assume both Jesse and the bus are moving at constant rates.

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After school, Jesse walks to a friend’s house, which is on the way home. He stays there until he takes a bus home. Which of the following graphs represent parts of Jesse’s trip to or from school? Assume both Jesse and the bus are moving at constant rates.

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Jesse walks from home to the bus stop. He pauses to check in his bag for his notebook. He runs back home to get his notebook. Which of the following graphs represent parts of Jesse’s trip to or from school? Assume both Jesse and the bus are moving at constant rates.

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