91Ó°ÊÓ

The equation for \(f\) is given by the simplified expression that results after performing the indicated operation. Write the equation for \(f\) and then graph the function. $$\frac{x-\frac{1}{x}}{x+\frac{1}{x}}$$

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. $$f(x)=3(x+2)^{2}-5 ; \quad(-1,-2)$$

Use long division to rewrite the equation for \(g\) in the form $$\text {quotient }+\frac{\text {remainder}}{\text {divisor}}$$ Then use this form of the function's equation and transformations. $$g(x)=\frac{2 x+7}{x+3}$$

Use long division to rewrite the equation for \(g\) in the form $$\text {quotient }+\frac{\text {remainder}}{\text {divisor}}$$ Then use this form of the function's equation and transformations. $$g(x)=\frac{3 x+7}{x+2}$$

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. $$f(x)=(x-3)^{2}+2 ; \quad(6,11)$$

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

Use long division to rewrite the equation for \(g\) in the form $$\text {quotient }+\frac{\text {remainder}}{\text {divisor}}$$ Then use this form of the function's equation and transformations. $$g(x)=\frac{3 x-7}{x-2}$$

Write the equation of each parabola in standard form. Vertex: \((-3,-4) ;\) The graph passes through the point \((1,4)\)

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

Write the equation of each parabola in standard form. Vertex: \((-3,-1) ;\) The graph passes through the point \((-2,-3)\)