Begin by graphing \( f(x)=3^{\wedge} \). Then use transformations of this graph to graph the given function: Be sure to graph and give the equation of the asymptote. Use the graph to determine the function's'domain and range. If applicable, use graphing utility to contirm your hand-drawn graphs. \[ g(x)=3^{x}-1 \] Graph \( g(x)=3^{x}-1 \) and its asymptote. Use the graphing tool to graph the function as a solid curve and the asymptote as a dashed line. Click to enlarge graph

(a) Express the distance \( d \) from \( P \) to the origin as a function of \( x \). \( d(x)=\sqrt{x^{4}-3 x^{2}+4} \) (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 2 . (Type an integer or decimal rounded to two decimal placels as needed.) (c) What is \( d \) if \( x=1 \) ? If \( x=1 \), the distance \( d \) is \( \square \). (Type an integer or decimal rounded to two decimal places as needed.)

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 \( k \).

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

Find the function that is finally graphed after the following transformations are applied to the graph of \( y=\sqrt{x} \) in the order listed. (1) Shift up 7 units (2) Reflect about the \( x \)-axis (3) Reflect about the \( y \)-axis \( y= \)

Given \( f(x)=\frac{-2}{x}-2 \), Answer the following questions: .1 Write down the equations of the asymptotes of \( f(x) \). 2 Draw a neat sketch graph of \( f(x) \), clearly indicate the asymptotes and the intercepts with the axes. .3 Write down the domain and range of \( f(x) \).