91Ó°ÊÓ

Sketch a rational function subject to the given conditions. Answers may vary. Horizontal asymptote: \(y=2\) Vertical asymptote: \(x=3\) \(y\) -intercept: \(\left(0, \frac{8}{3}\right)\) \(x\) -intercept: (4,0)

Sketch the function. \(k(x)=0.2(x+2)^{2}(x-4)^{3}\)

Sketch a rational function subject to the given conditions. Answers may vary. Horizontal asymptote: \(y=0\) Vertical asymptote: \(x=-1\) \(y\) -intercept: (0,1) No \(x\) -intercepts Range: \((0, \infty)\)

a. Factor \(f(x)=4 x^{3}-20 x^{2}+33 x-18\), given that 2 is a zero. b. Solve. \(4 x^{3}-20 x^{2}+33 x-18=0\)

Explain how to use the discriminant to determine the number of \(x\) -intercepts for the graph of \(f(x)=a x^{2}+b x+c\)

Sketch the function. \(m(x)=0.1(x-3)^{2}(x+1)^{3}\)

Determine if the statement is true or false. If 5 is an upper bound for the real zeros of \(f(x)\), then 4 is also an upper bound.

Write a polynomial \(f(x)\) that meets the given conditions. Answers may vary. (See Example 10 ) Degree 3 polynomial with zeros \(2,3,\) and -4

Sketch a rational function subject to the given conditions. Answers may vary. Horizontal asymptote \(y=0\) Vertical asymptotes \(x=-2\) and \(x=2\) \(y\) -intercept (0,1) No \(x\) -intercepts Symmetric to the \(y\) -axis Passes through the point \(\left(3,-\frac{4}{5}\right)\)

If a quadratic function given by \(y=f(x)\) has \(x\) -intercepts of (2,0) and \((6,0),\) explain why the vertex must be \((4, f(4))\).