Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 7) \( f(x)=-x^{2}(x+1)(x+3) \)

Given the function with the equation \( k(x)=\frac{-6}{x+2}-2 \) : \( 7.1 \quad \) Write the equations of the asymptotes of \( k \).

Complete the sentence below. Suppose that the graph of a function \( f \) is known. Then the graph of \( y=f(-x) \) may be obtained by a reflection about the -axis of the graph of the function \( y=f(x) \). Suppose that the graph of a function \( f \) is known. Then the graph of \( y=f(-x) \) may be obtained by a reflection about the -axis of the graph of the function \( y=f(x) \).

(a) Express the distance \( d \) from \( P \) to the origin as a function of \( x \). \( d(x)=\sqrt{\mathrm{x}^{4}-3 \mathrm{x}^{2}+4} \) (Simplify your answer. Type an exact answer, using radicals as needed.) (b) What is \( d \) if \( x=0 \) ? If \( x=0 \), the distance \( d \) is (Type an integer or decimal rounded to two decimal places as needed.)

Given: \( f(x)=2\left(x^{2}-1\right) \) Sketch function \( f \) on the diagram sheet. Clearly show all intercepts with the axes.

Let \( P=(x, y) \) be a point on the graph of \( y=x^{2}-2 \). Complete parts (a) through (e) below. (a) Express the distance \( d \) from \( P \) to the origin as a function of \( x \). \( d(x)= \) (Simplify your answer. Type an exact answer, using radicals as needed.)