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Chapter 3: Q. 103 (page 158)

Can a quadratic function have a range of(-鈭�,鈭�) ? Justify your answer.

Short Answer

Expert verified

No there does not exist a quadratic function whose range is of whole real numbers

Step by step solution

01

Given information

We are asked that is there a functionf(x)=ax2+bx+cwhose range is(-鈭�,鈭�)

02

Explanation

No. there does not exist a quadratic equation whose range is whole real numbers. It is not possible for a function to have range of whole real numbers There must be a minimum and maximum value that will be located at the functions vertex.

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Most popular questions from this chapter

Maximizing Revenue: The price p (in dollars) and the quantity x sold of a certain product obey the demand equation

x=-5p+100;0<p鈮�20

(a) Express the revenue R as a function of x.

(b) What is the revenue if 15 units are sold?

(c) What quantity x maximizes revenue? What is the maximum revenue?

(d) What price should the company charge to maximize revenue?

(e) What price should the company charge to earn at least $480 in revenue?

Under what circumstances is a linear function f(x)=mx+b odd? Can a linear function ever be even?

Artillery A projectile fired from the point (0, 0) at an angle

to the positive x-axis has a trajectory given by

y=cx-1+c2g2xv2

where

x = horizontal distance in meters

y = height in meters

v = initial muzzle velocity in meters per second (m/sec)

g = acceleration due to gravity = 9.81 meters per second squared m/sec2

c>0is a constant determined by the angle of elevation.

A howitzer fires an artillery round with a muzzle velocity of 897 m/sec.

(a) If the round must clear a hill 200 meters high at a distance of 2000 meters in front of the howitzer, what cvalues are permitted in the trajectory equation?

(b) If the goal in part (a) is to hit a target on the ground 75 kilometers away, is it possible to do so? If so, for what values of c? If not, what is the maximum distance the round will travel?

A rectangle has one vertex on the line y=10-x,x>0, another at the origin, one on the positive x-axis, and one on the positive y-axis. Express the area A of the rectangle as a function of x. Find the largest area A that can be enclosed by the rectangle.

Graph the function fby starting with the graph of y=x2and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

Hint: If necessary, write fin the form f(x)=a(x-h)2+k.

f(x)=2x2-4x+1
See all solutions

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