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Recitation 1.8-1.
● Inequalities
● Coordinate Geometry
● Lines
● Solving Equations & Inequalities Graphically
● 1.8-1.11 Review
● WebAssign Q&A
● Exam-level practice problems
● Quiz 3
1.8 Review - Inequalities
Example: Solve the inequality. Write your answer using interval notation.
2
1.10 - Lines
Example (SKIP) Write the equation of the line whose x-intercept is 6 and passes through the point
1.11 - Solving Equations & Inequalities Graphically
To solve an equation by graphing:
1. Move everything to one side (to find zeros)
2. Graph 𝑦 = 𝑓(𝑥)
3. 2nd → Calc → zero → set left bound → set right bound → guess
4. Repeat step 3 for each zero
Solve the following by graphing:
a. 𝑥^3 − 6𝑥^2 + 9𝑥 = 𝑥
3
2
- Determine the slope and x-intercept for the equation y=4.
Slope: 0 x-intercept: none
- The manager of a hotel knows that the daily number of rooms she can rent, N , is linearly related to the daily charge for the rooms, c. If she charges a daily rate of $75 per room, she can rent 180 rooms per day. If she charges a daily rate of $95, she can rent 80 rooms per day. Find an equation relating N and c so that N is a function of c. Then, use your model to predict the number of rooms rented if the daily charge is $100. Finally, explain what the slope means in non-technical terms.
55 rooms
- Biologists have observed that the chirping rate of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear. A cricket produces 120 chirps per minute at 70°F and 168 chirps per minute at 80°F.
(a) Find the linear equation that relates the temperature t and the number of chirps per minute n.
(b) If the crickets are chirping at 141 chirps per minute, estimate the temperature. (Round your answer to the nearest degree.)
1.8 and 1.
- How many solutions does each of the following inequalities have?
(a) 8 + 2|𝑥 − 4| > 7
Infinitely Many
(b) 7 + 2|𝑥 − 4| < 7
None
(c) 8 + 2|𝑥 − 4| < 7
None
- Solve 𝑥^2 (𝑥 − 4) < 0by providing an analysis of your solution. Include cutpoints and a number line and give your answer using interval notation.
- Find the domain of − 3𝑥^2 − 8𝑥 + 3. Show a complete analysis.
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Additional Mixed Practice (Time Permitting)
