Unit 2 – Lesson 1 – Investigation 1: Homework
1) Use the graph to answer the following questions.
a) Estimate the values for which 𝑓(𝑥) = 4 and express
the solution using interval and number line notation.
Interval notation
Number line notation
b) Estimate the values for which 𝑓(𝑥) ≥ 4 and express
the solution using interval and number line notation.
Interval notation
Number line notation
c) Estimate the values for which 𝑓(𝑥) < 4 and express the solution using interval and number line notation.
Interval notation
Number line notation
2) The graph shows the path of a football kick, with the height above the ground as a function of the distance
traveled (both in yards). The function defining the footballs path is: ℎ(𝑥) = −0.02𝑥 2 + 1.3𝑥 + 1.
For questions a - c write an inequality/equation that
represents the situation and then express the solution
using interval and number line notation.
a) When is the kicked ball exactly 20 yards above the
field?
Equation/Inequality:
Interval notation
Number line notation
b) When is the ball less than 10 yards above the playing field?
Equation/Inequality:
Interval notation
Number line notation
c) When is the ball at least 15 yards above the field?
Equation/Inequality:
Interval notation
d) How far is the ball above the field after it has traveled 40 yards?
Number line notation
3) The graph shows the depth of water alongside a ship pier in a tidal ocean harbor between 12 am and 12 pm
on one day. Suppose that 𝑑(𝑡) gives the depth in feet as a function of time.
For each part, write a question that represents the
given equation/inequality and then express the solution
using interval and number line notation where
appropriate.
a) Evaluate: 𝑑(2)
b) Solve: 𝑑(𝑡) = 40
Interval notation
Number line notation
c) Solve: 𝑑(𝑡) ≥ 40
Interval notation
Number line notation
d) Solve: 𝑑(𝑡) < 30
Interval notation
Number line notation
4) Use the following graph to answer the questions.
a) Solve: 𝑆(𝑛) ≥ −2
Interval notation
Number line notation
b) Solve: 𝑆(𝑛) < −2
Interval notation
Number line notation
c) Solve: 𝑆(𝑛) > −14
Interval notation
Number line notation