(Friday) Assignment: Problem Set
- Due No Due Date
- Points 10
- Submitting a file upload
Submit a copy of your work for each of the problem sets selected from Chapter 1.
Evaluating Functions
1. For the function f(x)=3x2+2x−1, evaluate
- f(−2)
- f(2‾√)
- f(a+h)
Finding Zeros and y-Intercepts of a Function
2. Consider the function f(x)=−4x+2.
- Find all zeros of f
- Find the y-intercept (if any).
- Sketch a graph of f.
A Linear Distance Function
3. Jessica leaves her house at 5:50 a.m. and goes for a 9-mile run. She returns to her house at 7:08 a.m. Answer the following questions, assuming Jessica runs at a constant pace.
a. Describe the distance D (in miles) Jessica runs as a linear function of her run time t (in minutes).
b. Sketch a graph of D.
c. Interpret the meaning of the slope.
Radian Measure
4. Express 210° using radians. Express 11π/6 rad using degrees.
5. Evaluate cos(3π/4) and sin(−π/6).
Finding an Inverse Function
6. Find the inverse for the function f(x)=3x−4. State the domain and range of the inverse function. Verify that f−1(f(x))=x.
Restricting Domain
7. Consider f(x)=1/x2 restricted to the domain (−∞,0). Verify that f is one-to-one on this domain. Determine the domain and range of the inverse of f and find a formula for f−1.
Exponential Functions: Bacterial Growth
8. Suppose a particular population of bacteria is known to double in size every 4 hours. If a culture starts with 1000 bacteria, the number of bacteria after 4 hours is n(4)=1000·2. The number of bacteria after 8 hours is n(8)=n(4)·2=1000·22. In general, the number of bacteria after 4m hours is n(4m)=1000·2m. Letting t=4m, we see that the number of bacteria after t hours is n(t)=1000·2t/4. Find the number of bacteria after 6 hours, 10 hours, and 24 hours.
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