Name: _____________________________
Date: ____________________
HW IM3 3.1.2
Block: ____
3-31. Solve (x – 3)2 – 2 = x + 1 graphically. Is there more than one way to do this?
Explain.
3-32. Make a complete graph of a system of equations to solve
Show your solutions clearly on your graph.
.
3-33. Solve each of the following equations using any method. Be sure to check your
solutions.
a.
b.
3-35. You decide to park your car in a parking garage that charges $3.00 for the first hour
and $1.00 for each hour (or any part of an hour) after that.
a. How much will it cost to park your car for 90 minutes?
b. How much will it cost to park your car for 118 minutes? 119 minutes?
c. How much will it cost to park your car for 120 minutes? 121 minutes?
d. Graph the cost in relation to the length of time
your car is parked.
e. Is this function continuous?
f. Describe how the graph of this function will
change if the parking garage raises their parking
rate so that the first hour costs $5.00.
3-36. Simplify each radical expression.
a.
b.
c.
d.
3-37. Sketch the graph of each function below on the same set of axes.
a. y = 2x
b. y = 2x + 5
c. y = 2x – 5
3-38. Solve 3x – 1 = 2x. Explain how you were able to solve.
3-39. Consider the graph of f(x) =
(x – 2)3 + 1 and g(x) = 2x2 – 6x – 3 at right.
a. Write an equation that you could solve using points A and B. What
are the solutions to your equation? Substitute them into your
equation to show that they work.
b. Are there any solutions to your equation in part (a) that do not
appear on the graph? Explain.
c. Write an equation that you could use to solve for the x-coordinate of point C.
Estimate the solution to your equation using the graph. Again, substitute your
solution into your equation. How close was your estimate?
3-42. If p(x) = x2 + 5x – 6:
a. Where does the graph of y = p(x) intersect the y-axis?
b. Where does the graph of y = p(x) intersect the x-axis?
c. If q(x) = x2 + 5x, what are the intercepts of the graph of y = q(x)?
d. Compare the graphs of p(x) and q(x).
e. What is p(x) – q(x)?
3-43. Make a complete graph of each of the following equations. (Keep the graphs
handy, because you will need them for your homework for Lesson 3.1.4.)
a.
b.
c. How are the two graphs similar? How are they different?
d. What are the domain and range of each graph?
3-44. Consider the system of equations below.
3y – 4x = –1
9y + 2x = 4
a.
Solve this system algebraically.
b.
Where do the graphs intersect?
c.
Explain the relationship between parts (a) and (b).