QUESTION 7 Given: \( f(x)=\frac{2}{x+4}-1 \) 7.1 Write down the equation of the asymptotes of \( f \). 7.2 Calculate the intercepts of the graph of \( f \) with the axes. 7.3 Sketch the graph of \( f \), showing clearly the asymptotes and intercepts with the axes. 7.4 Write down the coordinates of the image of the \( x \)-intercept if it is reflected about the axis of symmetry \( y=-x-5 \). 7.5 Write down the range of \( y=-f(x) \). Describe in words, the transformation of \( f \) to \( g \) if \( g(x)=\frac{-2}{x-4}-1 \).

(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.)

If \( (-1,8) \) is a point on the graph of \( y=f(x) \), which of the following must be on the graph of \( y=f(-x) \) ? \( (8,1) \) \( (-1,-8) \) Choose the correct answer below. \( (1,8) \) \( (-8,-1) \)

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 \( y=f(x) \).

Clearly indicate all intercepts with the axes as well as the QUESTION 7 Given the function with the equation \( k(x)=\frac{-6}{x+2}-2 \) : 7.1 Write the equations of the asymptotes of \( k \). 7.2 Give the range of \( k \). 7.3 Give the domain of \( k \).