91Ó°ÊÓ

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Every polynomial equation of degree 3 with real coefficients has at least one real root.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I like to think of a parabola's vertex as the point where it intersects its axis of symmetry.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm solving a polynomial inequality that has a value for which the polynomial function is undefined.

Explain why a polynomial function of degree 20 cannot cross the \(x\) -axis exactly once.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I began the solution of the rational inequality \(\frac{x+1}{x+3} \geq 2\) by setting both \(x+1\) and \(x+3\) equal to zero.

Use long division to rewrite the equation for \(g\) in the form quotient \(+\frac{\text { remainder }}{\text { divisor }}\) Then use this form of the function's equation and transformations of \(f(x)=\frac{1}{x}\) to graph \(g\) $$g(x)=\frac{2 x-9}{x-4}$$

Find the axis of symmetry for each parabola whose equation is given. Use the axis of symmetry to find a second point on the parabola whose y-coordinate is the same as the given point. $$f(x)=3(x+2)^{2}-5 ; \quad(-1,-2)$$

A company is planning to manufacture mountain bikes. The fixed monthly cost will be \(\$ 100,000\) and it will cost \(\$ 100\) to produce each bicycle. a. Write the cost function, \(C,\) of producing \(x\) mountain bikes. b. Write the average cost function, \(\bar{C},\) of producing \(x\) mountain bikes. c. Find and interpret \(\bar{C}(500), \bar{C}(1000), \bar{C}(2000),\) and \(\bar{C}(4000)\) d. What is the horizontal asymptote for the graph of the average cost function, \(C ?\) Describe what this means in practical terms.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The inequality \(\frac{x-2}{x+3}<2\) can be solved by multiplying both sides by \((x+3)^{2}, x \neq-3,\) resulting in the equivalent inequality \((x-2)(x+3)<2(x+3)^{2}\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm graphing a fourth-degree polynomial function with four turning points.