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Chapter 2: Q. 83 (page 114)

The equation y=x-c2defines a family of parabolas, one parabola for each value of c. On one set of coordinate axes, graph the members of the family for c=0,c=3and

c=-2.

Short Answer

Expert verified

The graph for the parabolas when c=0,c=-2,c=3is,

Step by step solution

01

Step1 Given values are, c=0,c=-2,c=3.

Given equation is, y=x-c2

Substitute c=0in the given equation.

y=x2which is the square function.

Substitute c=-2in the equation.

y=x+22, the graph of which is obtained by shifting the graph of y=x2to the left by 2units.

Substitute c=3in the equation.

y=x-32,the graph of which is obtained by shifting the graph ofy=x2to the right by3units.

02

Step 2 Now graph the obtained equations.

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Most popular questions from this chapter

In March 2011, Peoples Energy had the following rate schedule for natural gas usage in single- family residences:

Monthly service charge- \(18.95

Per therm service charge

1st50therms- \)0.33372/therm

Over 50therms- \(0.12360/therm

Gas charge- \)0.5038/therm

(a) What is the charge for using 50therms in a month?

(b) What is the charge for using 500therms in a month?

(c) Develop a model that relates the monthly charge Cfor xtherms of gas.

(d) Graph the function found in part (c)

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

h(x)=12x

True or False The domain of (f.g)(x)consists of the numbers x that are in the domains of both fandg.

Match each graph to its function.

A. Constant function

B. Identity function

C. Square function

D. Cube function

E. Square root function

F. Reciprocal function

G. Absolute value function

H. Cube root function

A circle of radius ris in inscribed in a square. See the figure.

Part (a): Express the area A of the square as a function of the radius rof the circle.

Part (b): Express the perimeter p of the square as a function of the radius rof the circle.
See all solutions

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