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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

In problems 3-6, use the figure to solve each inequality.

a) f(x)>0

b)f(x)鈮�0

Graph the function fby starting with the graph of y=x2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

f(x)=(x+2)2-2

If the independent variable in a line of best fit y=-0.008x+14is credit score, and the dependent variable is the interest rate on a used car loan, then the slope is interpreted as 鈥渋f credit score increases by 1 point, the interest rate will (increase/decrease) by percent, on average.

Find a quadratic function whose x-intercepts are -4 and 2 and whose range is[-18,鈭�)

The daily revenue R achieved by selling x boxes of candy is figured to be R(x)=9.5x-0.04x2The daily cost C of selling x boxes of candy is C(x)=1.25x+250.

(a) How many boxes of candy must the firm sell to maximize revenue? What is the maximum revenue?

(b) Profit is given as P(x) = R(x) - C(x). What is the profit function?

(c) How many boxes of candy must the firm sell to maximize profit? What is the maximum profit?

(d) Provide a reasonable explanation as to why the answers found in parts (a) and (c) differ. Explain why a quadratic function is a reasonable model for revenue.
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