Name: _______________________________________________
Algebra 1
Homework – Interpreting Function Notation Word Problems
1. In New York City the temperature is 61°F and is falling at a rate of 2°F per hour. The linear function that
models the temperature T is T(x) = 61 – 2x where x is the time in hours.
1.a. Explain what T(2) represents.
1.b. Find T(4). Explain what it represents.
1.c. If T(x) = 51, find x. Explain what this represents.
2. Carlos bought a tree that is 60 inches tall. The tree grows 1/4 inch per month. The linear model that
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represents this information is 𝐻(𝑡) = 60 + 4 𝑡, where H is the height in inches and t is the time in months.
2.a.) Explain what H(3) represents.
2.b.) Find H(8). Explain what it represents.
2.c.) Find t, such that H(t) = 63. Explain what this represents.
3. Fran is professional party planner. She charges a $250 initial fee and then $50 per hour to plan an event.
3.a. Write a function C(x) that represents Fran’s charges C in terms on the number of hours planning x.
3.b. Find C(4). Explain what it represents.
3.c. Find x such that C(x) = 750. Explain what this represents.
4. “Shifty” is a car rental store. “Shifty” charges an upfront fee of $25 and then $0.10 per mile driven.
4.a. Write a linear function C(d) equation that represents the charges C in terms of the distance driven d in
miles.
4.b. Find C(100). Explain what it represents.
4.c. If C(d) = 70, find d. Explain what this represents.
5. Simplify each expression by combining like terms.
5x – 9y + 11 + 6x + 8y – 15
5a – 20b – 5a – 20b
-6(x – 2) – 3y + 7
2(x – 9)
3x + 7x + 11x + 15 + 20
23 + 35x – (14x – 24)
6. Solve the linear equations below.
6(x + 3) = 6x + 18
3x – 7 – 9x – 5 = 4x + 5
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x + 8 = 32
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7. Chuck and Abraham are both climbing a mountain. Chuck starts from his camp which has an elevation of
500 feet and climbs 100 feet per hour. Abraham starts from his camp which has an elevation of 1000 feet, but
only climbs 50 feet per hour.
7.a. Write a linear function C(h) that represents Chuck’s height with respect to hours climbing.
7.b. Write a linear function A(h) that represents Abraham’s height with respect to hours climbing.
7.c. Write an equation and solve it to find how long to both men have to climb until there elevations will be the
same?
7.d. What is the elevation of the men when their elevations are the same?