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Chapter 2: Q. 45 (page 101)

If f(x)=int(2x), find

  1. f1.2
  2. f1.6
  3. f-1.8

Short Answer

Expert verified
  1. The value of f(1.2)is 2.
  2. The value of f(1.6)is 3.
  3. The value of f(-1.8)is -4.

Step by step solution

01

Step 1. Given Information

We are given a function,

f(x)=int(2x)

The greatest integer function gives the integer less than or equal to the given number.

02

Part(a) Step 1. Finding part(a)

Putting x=1.2in the given function, we get

f(x)=int(2x)f(1.2)=int(2(1.2))f(1.2)=int(2.4)

The greatest integer less than 2.4is 2, so

f(1.2)=2

03

Part(b) Step 1. Finding part(b)

Putting x=1.6 in the given function, we get

f(x)=int(2x)f(1.6)=int(2(1.6))f(1.6)=int(3.2)

The greatest integer less than 3.2is3, so

f(1.6)=3

04

Part(c) Step 1. Finding part(c) 

Putting x=-1.8 in the given function, we get

role="math" localid="1645892879987" f(x)=int(2x)f(-1.8)=int(2(-1.8))f(-1.8)=int(-3.6)

The greatest integer less than-3.6is-4, so

f(-1.8)=-4

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Most popular questions from this chapter

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

Suppose that the graph of a function fis known. Then the graph of y=f(-x) may be obtained by a reflection about the ________-axis of the graph of the function y=f(x).

Match each graph to its function.

A. Constant function

B. Identity function

C. Square function

D. Cube function

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F. Reciprocal function

G. Absolute value function

H. Cube root function

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)=2x3

Exploration Graph y=x2,y=x4, and y=x6 on the same screen. What do you notice is the same about each graph? What do you notice that is different?
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