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Chapter 2: Q. 21 (page 100)

Sketch the graph of each function. Be sure to label three points on the graph.

f(x)=1x

Short Answer

Expert verified

The graph is

Step by step solution

01

Step 1. Given information.

The given function is,

f(x)=1x.

02

Step 2. Finding the symmetry.

Now substituting x=-xin the given function then,

f(-x)=1-x=-1x=-f(x)

Therefore, the function is an odd function and symmetric with respect to the origin.

03

Step 3. Finding the ordered pairs.

Using the point plotting method we get,

x
y=f(x)=1x
x,y
-1
y=1-1=-1
-1,-1
1
y=11=1
1,1
2
y=12
2,12
04

Step 4. Plotting the points on a graph.

The graph is

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Most popular questions from this chapter

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

If f(x)=2x-4if-1≤x≤2x3-2if2<x≤3

Find: (a) f(0) (b) f(1) (c) f(2) (d)f(3)

Exploration Graph y=x3,y=x5, and y=x7 on the same screen. What do you notice is the same about each graph? What do you notice that is different?

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.g(x)=x3-1

A rectangle is inscribed in a semicircle of radius 2. See the figure. Let P=x,ybe the point in quadrant I that is vertex of the rectangle and is on the circle.

Part (a): Express the area A of the rectangle as a function of x.

Part (b): Express the perimeter pof the rectangle as a function of x.

Part (c): Graph A=Ax. For what value of xis Alargest?

Part (d): Graph p=px. For what value of xis plargest?
See all solutions

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